Ⅱ 식의 계산

익힘책 해설편

Ⅱ-1 식의 계산

선수 학습                                p. 43

1 (1) [eqn: 2 ^{3}]	(2) [eqn: 3 ^{4}]

(3) [eqn: 2 ^{3} TIMES 3 ^{2}]	(4) [eqn: 2 TIMES 3 ^{2} TIMES 5 ^{3}]

2 (1) [eqn: 2xy]	(2) [eqn: ab ^{2}]

(3) [eqn: {a} over {3}]	(4) [eqn: - {a+b} over {5}]

3 [eqn: LEFT ( 2a+1 RIGHT ) + LEFT ( 2a+2 RIGHT ) =4a+3]

4 (1) [eqn: a+2a= LEFT ( 1+2 RIGHT ) a=3a]

(2) [eqn: 3a+5+2a-4= LEFT ( 3+2 RIGHT ) a+ LEFT ( 5-4 RIGHT )]

[eqn: =5a+1]

(3) [eqn: 5x-2x+7= LEFT ( 5-2 RIGHT ) x+7=3x+7]

(4) [eqn: 3x+1-2 LEFT ( x+4 RIGHT ) =3x+1-2x-8=x-7]

5 (1) [eqn: 3a+b=3 TIMES 2+ LEFT ( -3 RIGHT ) =6-3=3]

(2) [eqn: 2 LEFT ( ab-3 RIGHT ) =2 LEFT { 2 TIMES LEFT ( -3 RIGHT ) -3 RIGHT }]

[eqn: =2 LEFT ( -6-3 RIGHT ) =-18]

(3) [eqn: a ^{2} +b ^{2} =2 ^{2} + LEFT ( -3 RIGHT ) ^{2} =4+9=13]

(4) [eqn: a LEFT ( -b+2 RIGHT ) =2 LEFT { - LEFT ( -3 RIGHT ) RIGHT } +2]

[eqn: =2 LEFT ( 3+2 RIGHT ) =10]

탐구 활동 또 알아보기	p. 44

[eqn: a ^{2} +ab+ba+b ^{2} =a ^{2} +2ab+b ^{2}]

탐구 활동 또 알아보기	p. 45

1 [eqn: a=140]일 때,

[eqn: h= {80} over {100} LEFT ( 200-140 RIGHT ) = {80} over {100} TIMES 60=48(점)]

2 [eqn: h= {80} over {100} LEFT ( 200-a RIGHT )], [eqn: {100} over {80} h=200-a]

[eqn: THEREFORE ``a=200- {100} over {80} h LEFT ( 또는~a=200- {5} over {4} h RIGHT )]

익힘 문제                            pp. 46~53

1 (1) [eqn: LEFT ( 4x+6 RIGHT ) + LEFT ( 2x-2 RIGHT ) =4x+6+2x-2]

[eqn: =6x+4]

(2) [eqn: LEFT ( 3x-y RIGHT ) + LEFT ( -5x+y RIGHT ) =3x-y-5x+y]

[eqn: =-2x]

(3) [eqn: LEFT ( 2x-4y RIGHT ) - LEFT ( x-y RIGHT ) =2x-4y-x+y]

[eqn: =x-3y]

(4) [eqn: LEFT ( 5x+2y RIGHT ) - LEFT ( -x+y RIGHT ) =5x+2y+x-y]

[eqn: =6x+y]

2 (1) [eqn: LEFT ( 2x ^{2} +3x-2 RIGHT ) + LEFT ( x ^{2} -2x+5 RIGHT )]

[eqn: =2x ^{2} +3x-2+x ^{2} -2x+5]

[eqn: =3x ^{2} +x+3]

(2) [eqn: LEFT ( x ^{2} +2x-1 RIGHT ) - LEFT ( -x ^{2} +3x-4 RIGHT )]

[eqn: =x ^{2} +2x-1+x ^{2} -3x+4]

[eqn: =2x ^{2} -x+3]

(3) [eqn: {5x ^{2} -4x+2} over {2} + LEFT ( x ^{2} -3x-1 RIGHT )]

[eqn: = {5} over {2} x ^{2} -2x+1+x ^{2} -3x-1= {7} over {2} x ^{2} -5x]

(4) [eqn: {6x ^{2} +3x+4} over {3} - {4x ^{2} +x+2} over {2}]

[eqn: =2x ^{2} +x+ {4} over {3} -2x ^{2} - {1} over {2} x-1]

[eqn: = {1} over {2} x+ {1} over {3}]

3 (1) [eqn: 5x+6y-3]

(2)

4 (1) [eqn: BOX{`````````````````} `=5x-2y+3- LEFT ( 3x+y-1 RIGHT )]

[eqn: =5x-2y+3-3x-y+1]

[eqn: =2x-3y+4]

(2) [eqn: BOX{`````````````````} `= {1} over {2} x+3y+2- LEFT ( x+ {1} over {3} y-1 RIGHT )]

[eqn: = {1} over {2} x+3y+2-x- {1} over {3} y+1]

[eqn: =- {1} over {2} x+ {8} over {3} y+3]

(3) [eqn: BOX{`````````````````} `=x ^{2} +4- LEFT ( 5x ^{2} -2x-1 RIGHT )]

[eqn: =x ^{2} +4-5x ^{2} +2x+1]

[eqn: =-4x ^{2} +2x+5]

(4) [eqn: BOX{`````````````````} `=2x ^{2} +x-4- LEFT ( -2x ^{2} +2x-3 RIGHT )]

[eqn: =2x ^{2} +x-4+2x ^{2} -2x+3]

[eqn: =4x ^{2} -x-1]

5 (1) [eqn: x ^{2} TIMES x ^{3} =x ^{2+3} =x ^{5}]

(2) [eqn: x ^{2} TIMES x ^{4} TIMES y ^{3} TIMES y ^{2} =x ^{2+4} TIMES y ^{3+2} =x ^{6} y ^{5}]

(3) [eqn: x ^{3} yz ^{2} TIMES x ^{2} y ^{4} z ^{3} =x ^{3} TIMES x ^{2} TIMES y TIMES y ^{4} TIMES z ^{2} TIMES z ^{3}]

[eqn: =x ^{3+2} TIMES y ^{1+4} TIMES z ^{2+3}]

[eqn: =x ^{5} y ^{5} z ^{5}]

(4) [eqn: LEFT ( x ^{2} RIGHT ) ^{6} TIMES LEFT ( y ^{3} RIGHT ) ^{4} =x ^{2 TIMES 6} TIMES y ^{3 TIMES 4} =x ^{12} y ^{12}]

6 (1) [eqn: x ^{12} ÷x ^{3} ÷x ^{5} =x ^{12-3-5} =x ^{4}]

(2) [eqn: LEFT ( x ^{2} RIGHT ) ^{5} ÷ LEFT ( x ^{4} RIGHT ) ^{3} =x ^{10} ÷x ^{12} = {1} over {x ^{12-10}} = {1} over {x ^{2}}]

(3) [eqn: LEFT ( x ^{2} y RIGHT ) ^{3} TIMES LEFT ( x ^{4} y ^{3} RIGHT ) ^{2} =x ^{6} y ^{3} TIMES x ^{8} y ^{6}]

[eqn: =x ^{6+8} y ^{3+6} =x ^{14} y ^{9}]

(4) [eqn: LEFT ( {-2x} over {y ^{2}} RIGHT ) ^{4} = {LEFT ( -2 RIGHT ) ^{4} x ^{4}} over {y ^{2 TIMES 4}} = {16x ^{4}} over {y ^{8}}]

7 (1) [eqn: LEFT ( -x ^{2} y RIGHT ) TIMES 3xy ^{4} TIMES LEFT ( -2xy ^{2} RIGHT ) ^{3}]

[eqn: = LEFT ( -x ^{2} y RIGHT ) TIMES 3xy ^{4} TIMES LEFT ( -8x ^{3} y ^{6} RIGHT )]

[eqn: = LEFT ( -1 RIGHT ) TIMES 3 TIMES LEFT ( -8 RIGHT ) TIMES x ^{2} TIMES x TIMES x ^{3} TIMES y TIMES y ^{4} TIMES y ^{6}]

[eqn: =24x ^{6} y ^{11}]

(2) [eqn: 6x ^{8} y ^{9} ÷2 LEFT ( xy ^{2} RIGHT ) ^{2} ÷ LEFT ( x ^{2} y RIGHT ) ^{3}]

[eqn: =6x ^{8} y ^{9} ÷2x ^{2} y ^{4} ÷x ^{6} y ^{3}]

[eqn: =6x ^{8} y ^{9} TIMES {1} over {2x ^{2} y ^{4}} TIMES {1} over {x ^{6} y ^{3}}]

[eqn: =3y ^{2}]

(3) [eqn: 8x ^{2} y ^{8} TIMES LEFT ( -x ^{3} y RIGHT ) ^{3} ÷ LEFT ( -xy RIGHT ) ^{2}]

[eqn: =8x ^{2} y ^{8} TIMES LEFT ( -x ^{9} y ^{3} RIGHT ) ÷x ^{2} y ^{2}]

[eqn: =8x ^{2} y ^{8} TIMES LEFT ( -x ^{9} y ^{3} RIGHT ) TIMES {1} over {x ^{2} y ^{2}}]

[eqn: =-8x ^{9} y ^{9}]

(4) [eqn: LEFT ( {2} over {3ab} RIGHT ) ^{2} ÷ LEFT ( {2} over {3} ab RIGHT ) ^{2} TIMES LEFT ( - {a} over {2b} RIGHT ) ^{3}]

[eqn: = {4} over {9a ^{2} b ^{2}} ÷ {4a ^{2} b ^{2}} over {9} TIMES LEFT ( - {a ^{3}} over {8b ^{3}} RIGHT )]

[eqn: = {4} over {9a ^{2} b ^{2}} TIMES {9} over {4a ^{2} b ^{2}} TIMES LEFT ( - {a ^{3}} over {8b ^{3}} RIGHT )][eqn: =- {1} over {8ab ^{7}}]

8 (1) [eqn: 3,~3]

(2) [eqn: BOX{````````} `=20`x ^{10} y ^{8} ÷ LEFT ( -10`x ^{6} y ^{6} RIGHT ) ÷2x ^{2}]

[eqn: =20`x ^{10} y ^{8} TIMES {1} over {-10`x ^{6} y ^{6}} TIMES {1} over {2x ^{2}}]

[eqn: =-x ^{2} y ^{2}]

(3) [eqn: BOX{````````} `=a ^{7} b ^{3} ÷12a ^{6} b ^{6} TIMES 4a ^{4} b ^{2}]

[eqn: =a ^{7} b ^{3} TIMES {1} over {12a ^{6} b ^{6}} TIMES 4a ^{4} b ^{2}]

[eqn: = {a ^{5}} over {3b}]

9 (1) [eqn: 3 LEFT ( 2x ^{2} -x+4 RIGHT ) =6x ^{2} -3x+12]

(2) [eqn: -4x LEFT ( 3x+y RIGHT ) =-12x ^{2} -4xy]

(3) [eqn: 5a LEFT ( a-2 RIGHT ) -3 LEFT ( a ^{2} +2a-1 RIGHT )]

[eqn: =5a ^{2} -10a-3a ^{2} -6a+3]

[eqn: =2a ^{2} -16a+3]

(4) [eqn: 3x LEFT ( -2x+y RIGHT ) + LEFT ( x+3y RIGHT ) LEFT ( -5x RIGHT )]

[eqn: =-6x ^{2} +3xy-5x ^{2} -15xy]

[eqn: =-11x ^{2} -12xy]

10 (1) ① [eqn: ab]          ② [eqn: 2a]

③ [eqn: b]           ④ [eqn: 2]

(2) [eqn: LEFT ( a+1 RIGHT ) LEFT ( b+2 RIGHT ) =①+②+③+④]

[eqn: =ab+2a+b+2]

11 (1) [eqn: LEFT ( 2x+3 RIGHT ) LEFT ( x-1 RIGHT )]

[eqn: =2x ^{2} -2x+3x-3]

[eqn: =2x ^{2} +x-3]

(2) [eqn: LEFT ( a-b RIGHT ) LEFT ( 2a+5b RIGHT )]

[eqn: =2a ^{2} +5ab-2ab-5b ^{2}]

[eqn: =2a ^{2} +3ab-5b ^{2}]

(3) [eqn: LEFT ( -3x+y RIGHT ) LEFT ( -4x-2y RIGHT )]

[eqn: =12x ^{2} +6xy-4xy-2y ^{2}]

[eqn: =12x ^{2} +2xy-2y ^{2}]

(4) [eqn: LEFT ( 2a+b RIGHT ) LEFT ( -3a+2b RIGHT )]

[eqn: =-6a ^{2} +4ab-3ab+2b ^{2}]

[eqn: =-6a ^{2} +ab+2b ^{2}]

12 (1) [eqn: -2,~-3y,~2x]

(2) [eqn: 6,~6]

(3) [eqn: 2y,~5xy]

13 ① [eqn: a ^{2}]   ② [eqn: 2a]    ③ [eqn: 2a]    ④ [eqn: 4]

따라서 사각형의 넓이는

[eqn: LEFT ( a+2 RIGHT ) LEFT ( a+2 RIGHT ) = LEFT ( a+2 RIGHT ) ^{2}]

[eqn: =①+②+③+④]

[eqn: =a ^{2} +2a+2a+4]

[eqn: =a ^{2} +4a+4]

14 (1) [eqn: LEFT ( x+3 RIGHT ) ^{2} =x ^{2} +6x+9]

(2) [eqn: LEFT ( x+4y RIGHT ) ^{2} =x ^{2} +8xy+16y ^{2}]

(3) [eqn: LEFT ( a+2b RIGHT ) ^{2} =a ^{2} +4ab+4b ^{2}]

(4) [eqn: LEFT ( 3a+4b RIGHT ) ^{2} = LEFT ( 3a RIGHT ) ^{2} +2 TIMES 3a TIMES 4b+ LEFT ( 4b RIGHT ) ^{2}]

[eqn: =9a ^{2} +24ab+16b ^{2}]

15 [eqn: LEFT ( a-b RIGHT ) LEFT ( a-b RIGHT ) =a ^{2} -2ab+b ^{2}]

16 (1) [eqn: LEFT ( x-3 RIGHT ) ^{2} =x ^{2} -6x+9]

(2) [eqn: LEFT ( x-2y RIGHT ) ^{2} =x ^{2} -4xy+4y ^{2}]

(3) [eqn: LEFT ( 2b-5 RIGHT ) ^{2} = LEFT ( 2b RIGHT ) ^{2} -2 TIMES 2b TIMES 5+25]

[eqn: =4b ^{2} -20b+25]

(4) [eqn: LEFT ( 2a-3b RIGHT ) ^{2} = LEFT ( 2a RIGHT ) ^{2} -2 TIMES 2a TIMES 3b+ LEFT ( 3b RIGHT ) ^{2}]

[eqn: =4a ^{2} -12ab+9b ^{2}]

17 (1) [eqn: b]

(2) 색칠한 부분의 넓이는

(사각형 [eqn: rmABCG]의 넓이)+(사각형 [eqn: rmCDEF]의 넓이)이므로

[eqn: a LEFT ( a-b RIGHT ) +b LEFT ( a-b RIGHT ) =a ^{2} -ab+ab-b ^{2}]

[eqn: =a ^{2} -b ^{2}]

18 (1) [eqn: LEFT ( x-3 RIGHT ) LEFT ( x+3 RIGHT ) =x ^{2} -9]

(2) [eqn: LEFT ( x+3y RIGHT ) LEFT ( x-3y RIGHT ) =x ^{2} -9y ^{2}]

(3) [eqn: LEFT ( 10-2a RIGHT ) LEFT ( 10+2a RIGHT ) =100-4a ^{2}]

(4) [eqn: LEFT ( -a+3b RIGHT ) LEFT ( a+3b RIGHT )]

[eqn: =- LEFT ( a-3b RIGHT ) LEFT ( a+3b RIGHT )]

[eqn: =- LEFT ( a ^{2} -9b ^{2} RIGHT )]

[eqn: =-a ^{2} +9b ^{2}]

19 (1) [eqn: LEFT ( x+4 RIGHT ) LEFT ( x+5 RIGHT )]

[eqn: =x ^{2} + LEFT ( 4+5 RIGHT ) x+4 TIMES 5]

[eqn: =x ^{2} +9x+20]

(2) [eqn: LEFT ( x+4y RIGHT ) LEFT ( x-2y RIGHT )]

[eqn: =x ^{2} + LEFT { 4+ LEFT ( -2 RIGHT ) RIGHT } xy+4y TIMES LEFT ( -2y RIGHT )]

[eqn: =x ^{2} +2xy-8y ^{2}]

20 (1) [eqn: LEFT ( x+ {1} over {2} RIGHT ) LEFT ( x+ {1} over {4} RIGHT )]

[eqn: =x ^{2} + LEFT ( {1} over {2} + {1} over {4} RIGHT ) x+ {1} over {2} TIMES {1} over {4}]

[eqn: =x ^{2} + {3} over {4} x+ {1} over {8}]

(2) [eqn: LEFT ( 2x+3 RIGHT ) LEFT ( 5x+4 RIGHT )]

[eqn: =10x ^{2} + LEFT ( 8+15 RIGHT ) x+12]

[eqn: =10x ^{2} +23x+12]

(3) [eqn: LEFT ( -x+2y RIGHT ) LEFT ( 4x-3y RIGHT )]

[eqn: =-4x ^{2} +11xy-6y ^{2}]

(4) [eqn: LEFT ( {1} over {2} x+3y RIGHT ) LEFT ( -2x+4y RIGHT )]

[eqn: =-x ^{2} -4xy+12y ^{2}]

21 (1) [eqn: 4,~4]          (2) [eqn: {1} over {2} x,~2xy]

(3) [eqn: 3,~13x]        (4) [eqn: 2y,~4x,~2xy]

22 (1) [eqn: 41 ^{2} = LEFT ( 40+1 RIGHT ) ^{2} =40 ^{2} +2 TIMES 40 TIMES 1+1 ^{2}]

[eqn: =1600+80+1=1681]

(2) [eqn: 3.1 TIMES 2.9= LEFT ( 3+0.1 RIGHT ) LEFT ( 3-0.1 RIGHT )]

[eqn: =3 ^{2} - LEFT ( 0.1 RIGHT ) ^{2} =9-0.01=8.99]

23 반지름의 길이가 [eqn: r~rmm]인 원의 넓이는 [eqn: pi r ^{2} ~rmm ^{2}]

따라서 반지름의 길이를 [eqn: 2~rmm] 더 늘리면 반지름의 길이는 [eqn: LEFT ( r+2 RIGHT ) ```` rm m]이므로

원의 넓이는

[eqn: pi LEFT ( r+2 RIGHT ) ^{2} = pi LEFT ( r ^{2} +4r+4 RIGHT ) ```` LEFT ( rm m ^{2} RIGHT )]

따라서 두 원의 넓이의 차는

[eqn: pi LEFT ( 4r+4 RIGHT ) ```` rm m ^{2}]

24 (1) [eqn: LEFT ( 6x ^{2} -4x RIGHT ) ÷2x= {6x ^{2} -4x} over {2x}]

[eqn: =3x-2]

(2) [eqn: LEFT ( 10a ^{3} -5a ^{2} b RIGHT ) ÷ LEFT ( -5a RIGHT ) = {10a ^{3} -5a ^{2} b} over {-5a}]

[eqn: =-2a ^{2} +ab]

(3) [eqn: LEFT ( 3a ^{3} b ^{3} +ab ^{2} RIGHT ) ÷ LEFT ( - {1} over {3} ab RIGHT )]

[eqn: = LEFT ( 3a ^{3} b ^{3} +ab ^{2} RIGHT ) TIMES LEFT ( - {3} over {ab} RIGHT )]

[eqn: =3a ^{3} b ^{3} TIMES LEFT ( - {3} over {ab} RIGHT ) +ab ^{2} TIMES LEFT ( - {3} over {ab} RIGHT )]

[eqn: =-9a ^{2} b ^{2} -3b]

(4) [eqn: LEFT ( x ^{4} -2x ^{2} RIGHT ) ÷ {x} over {4} = LEFT ( x ^{4} -2x ^{2} RIGHT ) TIMES {4} over {x}]

[eqn: =x ^{4} TIMES {4} over {x} -2x ^{2} TIMES {4} over {x}]

[eqn: =4x ^{3} -8x]

25 (1) [eqn: LEFT ( 4xy ^{2} -2x ^{2} y RIGHT ) ÷2xy- LEFT ( -5x ^{2} y ^{2} +15x ^{3} y RIGHT ) ÷5x ^{2} y]

[eqn: = LEFT ( {4xy ^{2}} over {2xy} - {2x ^{2} y} over {2xy} RIGHT ) - LEFT ( {-5x ^{2} y ^{2}} over {5x ^{2} y} + {15x ^{3} y} over {5x ^{2} y} RIGHT )]

[eqn: = LEFT ( 2y-x RIGHT ) - LEFT ( -y+3x RIGHT )]

[eqn: =2y-x+y-3x]

[eqn: =-4x+3y]

(2) [eqn: LEFT ( 12a ^{2} b-9a RIGHT ) ÷3a- LEFT ( 4a ^{2} b ^{2} -2ab RIGHT ) ÷2ab]

[eqn: = LEFT ( {12a ^{2} b} over {3a} - {9a} over {3a} RIGHT ) - LEFT ( {4a ^{2} b ^{2}} over {2ab} - {2ab} over {2ab} RIGHT )]

[eqn: = LEFT ( 4ab-3 RIGHT ) - LEFT ( 2ab-1 RIGHT )]

[eqn: =4ab-3-2ab+1]

[eqn: =2ab-2]

26 (1) [eqn: LEFT ( a ^{3} b+4a ^{2} b RIGHT ) ÷ {ab} over {2} + LEFT ( 3a ^{3} -12a ^{2} RIGHT ) TIMES {1} over {3a}]

[eqn: = LEFT ( a ^{3} b+4a ^{2} b RIGHT ) TIMES {2} over {ab} + LEFT ( 3a ^{3} -12a ^{2} RIGHT ) TIMES {1} over {3a}]

[eqn: = LEFT ( {2a ^{3} b} over {ab} + {8a ^{2} b} over {ab} RIGHT ) + LEFT ( {3a ^{3}} over {3a} - {12a ^{2}} over {3a} RIGHT )]

[eqn: = LEFT ( 2a ^{2} +8a RIGHT ) + LEFT ( a ^{2} -4a RIGHT )]

[eqn: =3a ^{2} +4a]

(2) [eqn: x LEFT ( 2x-3 RIGHT ) - LEFT ( 3x ^{3} y-6x ^{2} y RIGHT ) ÷3x ^{2} y]

[eqn: =2x ^{2} -3x- LEFT ( {3x ^{3} y} over {3x ^{2} y} - {6x ^{2} y} over {3x ^{2} y} RIGHT )]

[eqn: =2x ^{2} -3x- LEFT ( x-2 RIGHT )]

[eqn: =2x ^{2} -3x-x+2]

[eqn: =2x ^{2} -4x+2]

(3) [eqn: LEFT ( x ^{3} y+2x ^{3} y ^{2} RIGHT ) TIMES {1} over {x ^{2} y} - LEFT ( 5x ^{2} -10x RIGHT ) ÷5x]

[eqn: = LEFT ( x+2xy RIGHT ) - LEFT ( x-2 RIGHT )]

[eqn: =x+2xy-x+2]

[eqn: =2xy+2]

27 사다리꼴의 넓이는

[eqn: {1} over {2} TIMES LEFT ( a+2a RIGHT ) TIMES h= {3ah} over {2}]

따라서 [eqn: {3ah} over {2} =a ^{2} -3a]

[eqn: h= LEFT ( a ^{2} -3a RIGHT ) ÷ {3a} over {2} = LEFT ( a ^{2} -3a RIGHT ) TIMES {2} over {3a}]

[eqn: = {2a ^{2}} over {3a} - {6a} over {3a} = {2} over {3} a-2]

28 (1) [eqn: -2x+3y=-2x+3 LEFT ( 2x-5 RIGHT )]

[eqn: =-2x+6x-15]

[eqn: =4x-15]

(2) [eqn: 3x-2y-8=3x-2 LEFT ( 2x-5 RIGHT ) -8]

[eqn: =3x-4x+10-8]

[eqn: =-x+2]

(3) [eqn: {1} over {2} x+ {1} over {4} y+ {1} over {4}]

[eqn: = {1} over {2} x+ {1} over {4} LEFT ( 2x-5 RIGHT ) + {1} over {4}]

[eqn: = {1} over {2} x+ {1} over {2} x- {5} over {4} + {1} over {4}]

[eqn: =x-1]

(4) [eqn: 6x ^{2} -2xy+2y]

[eqn: =6x ^{2} -2x LEFT ( 2x-5 RIGHT ) +2 LEFT ( 2x-5 RIGHT )]

[eqn: =6x ^{2} -4x ^{2} +10x+4x-10]

[eqn: =2x ^{2} +14x-10]

29 (1) [eqn: 5x-y=5 LEFT ( a-3b RIGHT ) - LEFT ( 3a+b RIGHT )]

[eqn: =5a-15b-3a-b]

[eqn: =2a-16b]

(2) [eqn: -2x+3y=-2 LEFT ( a-3b RIGHT ) +3 LEFT ( 3a+b RIGHT )]

[eqn: =-2a+6b+9a+3b]

[eqn: =7a+9b]

(3) [eqn: 3x-2 LEFT ( x-y RIGHT ) =3x-2x+2y]

[eqn: =x+2y]

[eqn: = LEFT ( a-3b RIGHT ) +2 LEFT ( 3a+b RIGHT )]

[eqn: =a-3b+6a+2b]

[eqn: =7a-b]

(4) [eqn: {x} over {3} + {y} over {2} = {2x} over {6} + {3y} over {6}]

[eqn: = {2 LEFT ( a-3b RIGHT ) +3 LEFT ( 3a+b RIGHT )} over {6}]

[eqn: = {2a-6b+9a+3b} over {6}]

[eqn: = {11a-3b} over {6} = {11} over {6} a- {1} over {2} b]

30 (1) [eqn: 3x-4y=2x+5y-4,]

[eqn: 3x-2x=5y+4y-4]

[eqn: THEREFORE ``x=9y-4]

(2) [eqn: 2x=3 LEFT ( y+x RIGHT ) ,~2x=3y+3x,]

[eqn: -3y=3x-2x,~-3y=x]

[eqn: THEREFORE ``y=- {1} over {3} x]

(3) [eqn: 10b ^{2} =2ab-4b,~2ab=10b ^{2} +4b,]

[eqn: a= {10b ^{2} +4b} over {2b}]   [eqn: THEREFORE ``a=5b+2]

(4) [eqn: 2ab-a+4=0,~2ab=a-4,]

[eqn: b= {a-4} over {2a} ,~b= {a} over {2a} - {4} over {2a}]

[eqn: THEREFORE ``b=- {2} over {a} + {1} over {2}]

31 (1) [eqn: LEFT ( 원뿔의~겉넓이 RIGHT ) = LEFT ( 밑넓이 RIGHT ) + LEFT ( 옆넓이 RIGHT )]

[eqn: S= pi r ^{2} + {1} over {2} TIMES 2 pi r TIMES l= pi r ^{2} + pi rl]

[eqn: S= pi r ^{2} + pi rl]을 [eqn: l]에 관하여 풀면

[eqn: pi rl=S- pi r ^{2} ,~l= {S- pi r ^{2}} over {pi r}]

[eqn: THEREFORE ``l= {S} over {pi r} -r]

(2) [eqn: LEFT ( 원뿔의~부피 RIGHT ) = {1} over {3} TIMES LEFT ( 밑넓이 RIGHT ) TIMES LEFT ( 높이 RIGHT )]

[eqn: V= {1} over {3} TIMES pi r ^{2} TIMES h]

[eqn: V= {1} over {3} pi r ^{2} h]를 [eqn: h]에 관하여 풀면

[eqn: 3V= pi r ^{2} h]   [eqn: THEREFORE ``h= {3V} over {pi r ^{2}}]

계산력 기르기                       pp. 54~55

① [eqn: x ^{3} y TIMES xy ^{2} =x ^{4} y ^{3}]

② [eqn: LEFT ( x ^{5} RIGHT ) ^{3} TIMES LEFT ( y ^{2} RIGHT ) ^{6} =x ^{15} y ^{12}]

③ [eqn: LEFT ( xy ^{2} RIGHT ) ^{3} TIMES LEFT ( x ^{3} y RIGHT ) ^{2} =x ^{3} y ^{6} TIMES x ^{6} y ^{2} =x ^{9} y ^{8}]

④ [eqn: 2x ^{2} y ^{3} TIMES LEFT ( -xy RIGHT ) ^{2} ÷x ^{2} y=2x ^{2} y ^{3} TIMES x ^{2} y ^{2} ÷x ^{2} y]

[eqn: =2x ^{2} y ^{4}]

⑤ [eqn: x ^{5} y ^{4} ÷x ^{3} y ^{3} =x ^{2} y]

⑥ [eqn: 3x ^{2} y ^{3} TIMES LEFT ( 2xy ^{2} RIGHT ) ^{3} ÷ LEFT ( -4x ^{2} y RIGHT ) ^{2}]

[eqn: =3x ^{2} y ^{3} TIMES 8x ^{3} y ^{6} ÷16x ^{4} y ^{2} = {3} over {2} xy ^{7}]

⑦ [eqn: 6xy ^{5} TIMES {x} over {3y ^{2}} ÷ LEFT ( -2xy ^{3} RIGHT ) ^{2}]

[eqn: =6xy ^{5} TIMES {x} over {3y ^{2}} TIMES {1} over {4x ^{2} y ^{6}}][eqn: = {1} over {2y ^{3}}]

⦁ 평양감사향연도

① [eqn: LEFT ( x+3 RIGHT ) ^{2} =x ^{2} +6x+9]

② [eqn: LEFT ( 2x-5 RIGHT ) ^{2} =4x ^{2} -20x+25]

③ [eqn: LEFT ( x+4 RIGHT ) LEFT ( x-4 RIGHT ) =x ^{2} -16]

④ [eqn: LEFT ( -3a+x RIGHT ) LEFT ( 3a+x RIGHT ) =-9a ^{2} +x ^{2}]

⑤ [eqn: LEFT ( x+3 RIGHT ) LEFT ( x-5 RIGHT ) =x ^{2} -2x-15]

⑥ [eqn: LEFT ( 2x-1 RIGHT ) LEFT ( 3x+2 RIGHT ) =6x ^{2} +x-2]

⑦ [eqn: LEFT ( 2x+3y RIGHT ) LEFT ( x-2y RIGHT ) =2x ^{2} -xy-6y ^{2}]

⦁ 신윤복, 연소답청

연습 문제                            pp. 56~57

1 [eqn: LEFT ( x ^{2} y-2xy ^{2} RIGHT ) ÷xy+ {xy-3y ^{2}} over {y}]

[eqn: = {x ^{2} y-2xy ^{2}} over {xy} + {xy-3y ^{2}} over {y}]

[eqn: =x-2y+x-3y]

[eqn: =2x-5y]

[eqn: THEREFORE ``A=2,~B=-5]

[eqn: THEREFORE ``A+B=-3]

2 [eqn: LEFT ( x ^{3} RIGHT ) ^{2} TIMES x ^{2} ÷ LEFT ( x ^{3} RIGHT ) ^{3} =x ^{6} TIMES x ^{2} ÷x ^{9} = {1} over {x ^{9-8}} = {1} over {x}]

㉠ [eqn: x ^{6} ÷x ^{5} =x ^{6-5} =x]

㉡ [eqn: LEFT ( x ^{3} RIGHT ) ^{4} ÷x ^{12} TIMES x=x ^{12} ÷x ^{12} TIMES x=x]

㉢ [eqn: x ^{12} ÷ LEFT ( x ^{2} RIGHT ) ^{5} ÷x ^{3} =x ^{12} ÷x ^{10} ÷x ^{3} = {1} over {x}]

㉣ [eqn: LEFT ( {1} over {x ^{2}} RIGHT ) ^{4} TIMES LEFT ( x ^{2} RIGHT ) ^{3} = {1} over {x ^{8}} TIMES x ^{6} = {1} over {x ^{2}}]

㉤ [eqn: LEFT ( x ^{2} RIGHT ) ^{5} TIMES LEFT ( {1} over {x ^{4}} RIGHT ) ^{3} ÷ {1} over {x} =x ^{10} TIMES {1} over {x ^{12}} TIMES x= {1} over {x}]

㉥ [eqn: x ^{3} TIMES x ^{4} ÷ {1} over {x ^{6}} =x ^{3} TIMES x ^{4} TIMES x ^{6} =x ^{13}]

따라서 ㉢, ㉤이다.

3  [eqn: LEFT ( x-3 RIGHT ) ^{2} + LEFT ( -2x+1 RIGHT ) LEFT ( 2x+1 RIGHT ) + LEFT ( 4x-3 RIGHT ) LEFT ( x+7 RIGHT )]

[eqn: = LEFT ( x ^{2} -6x+9 RIGHT ) - LEFT ( 4x ^{2} -1 RIGHT ) +4x ^{2} +25x-21]

[eqn: =x ^{2} +19x-11]

[eqn: THEREFORE ```A+B+C=1+19+ LEFT ( -11 RIGHT ) =9]

4 [eqn: 4ab+2b ^{2} =80,~2ab+b ^{2} =40,]

[eqn: `2ab=40-b ^{2}]

[eqn: THEREFORE ``a= {40-b ^{2}} over {2b} = {20} over {b} - {b} over {2}]

[eqn: a-b]	㉠	[eqn: a+c]
[eqn: a+b+c]	[eqn: a]	㉡
㉢	[eqn: a-b+c]	[eqn: a+b]

5 대각선의 합 [eqn: LEFT ( a-b RIGHT ) +a+ LEFT ( a+b RIGHT ) =3a]이므로

[eqn: ㉠:~a+b-c,````㉡:~a-b-c,````㉢:~a-c]

6 [eqn: 298 ^{2} = LEFT ( 300-2 RIGHT ) ^{2}]

[eqn: =300 ^{2} -2 TIMES 300 TIMES 2+2 ^{2}]

[eqn: =90000-1200+4=88804]

기초

7 (1) [eqn: LEFT ( 2x ^{2} -3x+1 RIGHT ) + LEFT ( x ^{2} +5x-4 RIGHT )]

[eqn: =2x ^{2} -3x+1+x ^{2} +5x-4]

[eqn: =3x ^{2} +2x-3]

(2) [eqn: LEFT ( 3x+y-2 RIGHT ) - LEFT ( x-2y+1 RIGHT )]

[eqn: =3x+y-2-x+2y-1]

[eqn: =2x+3y-3]

(3) [eqn: -2x LEFT ( x-y RIGHT ) +3x LEFT ( 2x-3y-1 RIGHT )]

[eqn: =-2x ^{2} +2xy+6x ^{2} -9xy-3x]

[eqn: =4x ^{2} -7xy-3x]

(4) [eqn: LEFT ( 8ab-4a ^{2} RIGHT ) ÷4a- LEFT ( 3a+6b RIGHT ) ÷3]

[eqn: = {8ab-4a ^{2}} over {4a} - {3a+6b} over {3}]

[eqn: =2b-a-a-2b=-2a]

8 (1) [eqn: a ^{2} b ^{3} c TIMES a ^{4} bc ^{2} =a ^{6} b ^{4} c ^{3}]

(2) [eqn: LEFT ( x ^{4} RIGHT ) ^{2} ÷ LEFT ( x ^{2} RIGHT ) ^{3} =x ^{8} ÷x ^{6} =x ^{8-6} =x ^{2}]

9 (1) [eqn: LEFT ( x+5 RIGHT ) ^{2} =x ^{2} +10x+25]

(2) [eqn: LEFT ( 2x-y RIGHT ) ^{2} =4x ^{2} -4xy+y ^{2}]

(3) [eqn: LEFT ( x+3 RIGHT ) LEFT ( x+1 RIGHT ) =x ^{2} +4x+3]

(4) [eqn: LEFT ( 3a-1 RIGHT ) LEFT ( 3a+1 RIGHT ) =9a ^{2} -1]

10 (1) [eqn: x-y+4=1,~x=y-3]

(2) [eqn: 2x-3y=x+2y-5,] [eqn: -5y=-x-5]     [eqn: THEREFORE ``y= {x} over {5} +1]

심화

11 분해한 각 부분의 부피

(ⅰ) [eqn: a ^{2} TIMES h=a ^{2} h]

(ⅱ) [eqn: a TIMES LEFT ( b-a RIGHT ) TIMES h TIMES {1} over {2} = {LEFT ( ab-a ^{2} RIGHT ) h} over {2}]

(ⅲ) [eqn: LEFT ( b-a RIGHT ) ^{2} TIMES h TIMES {1} over {3} = {LEFT ( b ^{2} -2ab+a ^{2} RIGHT ) h} over {3}]

사각뿔대의 부피는 (ⅰ)+(ⅱ)+(ⅱ)+(ⅲ)이므로

[eqn: a ^{2} h+2 TIMES {LEFT ( ab-a ^{2} RIGHT ) h} over {2} + {LEFT ( b ^{2} -2ab+a ^{2} RIGHT ) h} over {3}]

[eqn: =abh+ {b ^{2} h-2abh+a ^{2} h} over {3}]

[eqn: = {3abh+b ^{2} h-2abh+a ^{2} h} over {3}]

[eqn: = {a ^{2} h+abh+b ^{2} h} over {3}]

서술형 맛보기                            p. 58

어떻게 써야 할까?	배점
[eqn: p- {60} over {100} p=p- {3} over {5} p= {2} over {5} p]	3점
[eqn: a= {2} over {5} p+ {2} over {5} p TIMES {t} over {100} = {2} over {5} p+ {t} over {250} p= {100+t} over {250} p]	4점
[eqn: p= {250a} over {100+t}]	3점
총점	10점

따라해 보기

[eqn: q- {40} over {100} q=q- {2} over {5} q= {3} over {5} q]

3점

[eqn: b= {3} over {5} q+ {3} over {5} q TIMES {t} over {100} = {3} over {5} q+ {3t} over {500} q]

[eqn: = {300+3t} over {500} q]

4점

[eqn: THEREFORE ``q= {500b} over {300+3t}]

3점

평가 문제                            pp. 59~60

1 ②	2 ③	3 ②	4 ①	5 ④

6 ④	7 ⑤	8 ⑤     9 ③     10 ③

11 ④	12 ②	단답·서술형은 풀이 참조

1 [eqn: x- LEFT [ 7y+3x- LEFT { 4x+ LEFT ( 2x-y RIGHT ) RIGHT } RIGHT ]]

[eqn: =x- LEFT { 7y+3x- LEFT ( 6x-y RIGHT ) RIGHT }]

[eqn: =x- LEFT ( -3x+8y RIGHT )]

[eqn: =x+3x-8y]

[eqn: =4x-8y]

2 [eqn: BOX{``````````````````````````} ``=4x-5y+1-3 LEFT ( x-y+2 RIGHT )]

[eqn: =4x-5y+1-3x+3y-6]

[eqn: =x-2y-5]

3 [eqn: 2x LEFT ( x-3y RIGHT ) - LEFT ( x-2y RIGHT ) LEFT ( -3y RIGHT )]

[eqn: =2x ^{2} -6xy- LEFT ( -3xy+6y ^{2} RIGHT )]

[eqn: =2x ^{2} -6xy+3xy-6y ^{2}]

[eqn: =2x ^{2} -3xy-6y ^{2}]

따라서 [eqn: xy]의 계수는 [eqn: -3]

4 [eqn: {2 LEFT ( x-y RIGHT )} over {3} - {x-2y} over {2}]

[eqn: = {4 LEFT ( x-y RIGHT )} over {6} - {3 LEFT ( x-2y RIGHT )} over {6}]

[eqn: = {4x-4y-3x+6y} over {6}]

[eqn: = {x} over {6} + {y} over {3}]

5 어떤 식을 [eqn: A]라고 하면

[eqn: LEFT ( x ^{2} -2x+3 RIGHT ) -A=x-1]

[eqn: A= LEFT ( x ^{2} -2x+3 RIGHT ) - LEFT ( x-1 RIGHT ) =x ^{2} -3x+4]

[eqn: LEFT ( x ^{2} -2x+3 RIGHT ) + LEFT ( x ^{2} -3x+4 RIGHT ) =2x ^{2} -5x+7]

[eqn: THEREFORE ``A+B+C=2+ LEFT ( -5 RIGHT ) +7=4]

6 [eqn: {4x ^{2} y-12xy ^{2} +8xy} over {-4xy} - {2x ^{2} y ^{2} -4x ^{3} y} over {2x ^{2} y}]

[eqn: =-x+3y-2-y+2x]

[eqn: =x+2y-2]

[eqn: x=-2,~y=2]를 [eqn: x+2y-2]에 대입하면

[eqn: LEFT ( -2 RIGHT ) +2 TIMES 2-2=0]

7 ① [eqn: LEFT ( x ^{5} RIGHT ) ^{2} =x ^{5 TIMES 2} =x ^{10}]

② [eqn: x ^{3} TIMES x ^{7} =x ^{3+7} =x ^{10}]

③ [eqn: LEFT ( a ^{4} RIGHT ) ^{2} TIMES a ^{2} =a ^{4 TIMES 2+2} =a ^{10}]

④ [eqn: a ^{2} ÷a ^{4} TIMES {1} over {a} = {1} over {a ^{2}} TIMES {1} over {a} = {1} over {a ^{3}}]

8 [eqn: 72=2 TIMES 2 TIMES 2 TIMES 3 TIMES 3=2 ^{3} TIMES 3 ^{2}]

[eqn: 72 ^{3} = LEFT ( 2 ^{3} TIMES 3 ^{2} RIGHT ) ^{3} = LEFT ( 2 ^{3} RIGHT ) ^{3} TIMES LEFT ( 3 ^{2} RIGHT ) ^{3}]

[eqn: = LEFT ( A ^{3} RIGHT ) ^{3} TIMES LEFT ( B ^{2} RIGHT ) ^{3} =A ^{9} B ^{6}]

[eqn: THEREFORE ``m=9,~n=6]

[eqn: THEREFORE ``m+n=15]

9 [eqn: LEFT ( x-2y RIGHT ) ^{2} =x ^{2} -2 TIMES x TIMES 2y+4y ^{2}]

[eqn: =x ^{2} -4xy+4y ^{2}]

[eqn: =x ^{2} +Axy+By ^{2}]

[eqn: THEREFORE ``A=-4,~B=4]

[eqn: THEREFORE ``A+B= LEFT ( -4 RIGHT ) +4=0]

10 ㉠ [eqn: 3 ^{2} TIMES 3 ^{3} =3 ^{5}]

㉡ [eqn: 3 ^{2} TIMES 3÷ {1} over {3 ^{3}} =3 ^{2} TIMES 3 TIMES 3 ^{3} =3 ^{6}]

㉢ [eqn: LEFT ( 3 ^{4} RIGHT ) ^{3} ÷3 ^{2} =3 ^{12} ÷3 ^{2} =3 ^{10}]

㉣ [eqn: 3 ^{8} TIMES {1} over {3 ^{3}} ÷3 ^{2} =3 ^{5} ÷3 ^{2} =3 ^{3}]

㉤ [eqn: 3 ^{5} ÷3 ^{8} TIMES 3 ^{3} = {1} over {3 ^{3}} TIMES 3 ^{3} =1]

따라서 큰 순서로 나열하면 ㉢, ㉡, ㉠, ㉣, ㉤

11 ④ [eqn: LEFT ( a-b RIGHT ) LEFT ( a+b RIGHT ) - LEFT ( a-b RIGHT ) ^{2}]

[eqn: =a ^{2} -b ^{2} - LEFT ( a ^{2} -2ab+b ^{2} RIGHT )]

[eqn: =2ab-2b ^{2}]

12 ② [eqn: b= {ac} over {a-b} ,~ac=b LEFT ( a-b RIGHT ) ,~c= {ab-b ^{2}} over {a}]

[eqn: THEREFORE ``c=b- {b ^{2}} over {a}]

■단답·서술형■

13 [eqn: 999 ^{2} = LEFT ( 1000-1 RIGHT ) ^{2}]

5점

[eqn: =1000 ^{2} -2 TIMES 1000 TIMES 1+1 ^{2}]

2점

[eqn: =1000000-2000+1=998001]

3점

14 [eqn: LEFT ( {x ^{a} y ^{2} z ^{c}} over {x ^{4} y ^{b} z ^{5}} RIGHT ) ^{3} = {x ^{3a} y ^{6} z ^{3c}} over {x ^{12} y ^{3b} z ^{15}} = {x ^{3}} over {y ^{9} z ^{6}}]

3점

[eqn: THEREFORE ``x ^{3a-12} =x ^{3} ,~y ^{3b-6} =y ^{9} ,~z ^{15-3c} =z ^{6}]

5점

즉, [eqn: 3a-12=3]

[eqn: 3b-6=9]

[eqn: 15-3c=6]

[eqn: THEREFORE ``a=5,~b=5,````c=3]

2점

15 (1) [eqn: h=20000 TIMES t=20000t(원)]

4점

(2) [eqn: c=a+h,~h=20000t]이므로

[eqn: c=a+20000t(원)]

6점

16 [eqn: S= {1} over {2} TIMES {12} over {10} a TIMES {5} over {10} h]

5점

[eqn: S= {3} over {10} ah,~3ah=10S]

[eqn: THEREFORE ``h= {10S} over {3a}]

5점

종합 문제                            pp. 62~63

1 (1) [eqn: BOX{````````````````````````} `=3x-y+5- LEFT ( 2x-y+1 RIGHT )]

[eqn: =3x-y+5-2x+y-1]

[eqn: =x+4]

(2) [eqn: 4,~6]

2 (1) [eqn: y LEFT ( b-2x RIGHT )]

(2) 동규: (큰 사각형의 넓이)-(파란색 사각형의 넓이)

채은:

정현:

(3) 동규: [eqn: ab-y LEFT ( b-2x RIGHT ) =ab-by+2xy]

채은: [eqn: 2xy+b LEFT ( a-y RIGHT ) =2xy+ab-by]

정현: [eqn: 2ax+ LEFT ( a-y RIGHT ) LEFT ( b-2x RIGHT )]

[eqn: =2ax+ab-2ax-by+2xy]

[eqn: =ab-by+2xy]

따라서 세 식 모두 [eqn: ab-by+2xy]

3 (1) [eqn: LEFT ( 2x+3y RIGHT ) ^{2} =4x ^{2} +2 TIMES 2x TIMES 3y+9y ^{2}]

[eqn: =4x ^{2} +12xy+9y ^{2}]

[eqn: THEREFORE ``12]

(2) [eqn: LEFT ( x+ BOX{````````````} RIGHT ) LEFT ( x+5 RIGHT )]

[eqn: =x ^{2} + LEFT ( BOX{````````````} +5 RIGHT ) x+5 TIMES BOX{````````````}]

[eqn: =x ^{2} +7x+10]

[eqn: BOX{````````````} `+5=7,~5 TIMES BOX{````````````} `=10]에서 [eqn: BOX{````````````} `=2]

(3) [eqn: 49 ^{2} = LEFT ( 50-1 RIGHT ) ^{2} =50 ^{2} -2 TIMES 50 TIMES 1+1 ^{2}]

[eqn: =2500- BOX{``100``} +1= BOX{``2401``}]

[eqn: THEREFORE ``100,~2401]

4 (1) [eqn: 2x-3y=2 LEFT ( {a-2b} over {2} RIGHT ) -3 LEFT ( {a+b-1} over {3} RIGHT )]

[eqn: = LEFT ( a-2b RIGHT ) - LEFT ( a+b-1 RIGHT )]

[eqn: =-3b+1]

(2) [eqn: x+6y-4]

[eqn: = LEFT ( {a-2b} over {2} RIGHT ) +6 LEFT ( {a+b-1} over {3} RIGHT ) -4]

[eqn: = {a} over {2} -b+2a+2b-2-4= {5} over {2} a+b-6]

기초

5 (1) [eqn: 3 LEFT ( a+b RIGHT ) +2 LEFT ( a-2b RIGHT )]

[eqn: =3a+3b+2a-4b=5a-b]

(2) [eqn: LEFT ( 2x ^{2} -x+1 RIGHT ) - LEFT ( x ^{2} +4x-5 RIGHT )]

[eqn: =x ^{2} -5x+6]

6 (1) [eqn: LEFT ( a+ {1} over {2} b RIGHT ) ^{2} =a ^{2} +ab+ {1} over {4} b ^{2}]

(2) [eqn: LEFT ( a-5 RIGHT ) LEFT ( a+5 RIGHT ) =a ^{2} -5 ^{2} =a ^{2} -25]

(3)[eqn: LEFT ( x-3 RIGHT ) LEFT ( x-4 RIGHT ) =x ^{2} -7x+12]

(4) [eqn: LEFT ( 2x+3 RIGHT ) (3x-5)=6x ^{2} -10x+9x-15]

[eqn: =6x ^{2} -x-15]

7 (1) [eqn: LEFT ( 4x ^{2} +2x RIGHT ) ÷2x= {4x ^{2} +2x} over {2x}]

[eqn: = {4x ^{2}} over {2x} + {2x} over {2x} =2x+1]

(2) [eqn: LEFT { LEFT ( x ^{2} y RIGHT ) ^{2} + LEFT ( 2xy RIGHT ) ^{3} RIGHT } ÷x ^{3} y ^{2} = {x ^{4} y ^{2} +8x ^{3} y ^{3}} over {x ^{3} y ^{2}}]

[eqn: = {x ^{4} y ^{2}} over {x ^{3} y ^{2}} + {8x ^{3} y ^{3}} over {x ^{3} y ^{2}}]

[eqn: =x+8y]

심화

8 어떤 식을 [eqn: BOX{````````} `]라 하면 [eqn: LEFT ( 3xy-6y RIGHT ) ÷ BOX{```````````````````} `=3y]

[eqn: BOX{````````````````````} `= LEFT ( 3xy-6y RIGHT ) ÷3y= LEFT ( 3xy-6y RIGHT ) TIMES {1} over {3y}]

[eqn: =x-2]

바르게 계산하면

[eqn: LEFT ( 3xy-6y RIGHT ) TIMES LEFT ( x-2 RIGHT )]

[eqn: =3x ^{2} y-6xy-6xy+12y]

[eqn: =3x ^{2} y-12xy+12y]

9 물탱크 안쪽의 가로, 세로, 높이는 각각
[eqn: a-2y,~b-2x,~10c-c=9c]이므로
[eqn: LEFT ( 밑면의~넓이 RIGHT ) = LEFT ( a-2y RIGHT ) LEFT ( b-2x RIGHT )]

[eqn: =ab-2ax-2by+4xy` LEFT ( rmcm ^{2} RIGHT )]
[eqn: LEFT ( 부피 RIGHT ) = LEFT ( ab-2ax-2by+4xy RIGHT ) TIMES 9c]

[eqn: =9abc-18acx-18bcy+36cxy` LEFT ( rmcm ^{3} RIGHT )]