问题 解答题

因式分

(1)(a+b)x2-(a+b);

(2)9(a+b)2-4(a-b)2

(3)6xy2-9x2y-y3

(4)4+12(x-y)+9(x-y)2

答案

(1)(a+b)x2-(a+b)

=(a+b)(x2-1)

=(a+b)(x+1)(x-1);

(2)9(a+b)2-4(a-b)2

=[3(a+b)+2(a-b)][3(a+b)-2(a-b)]

=(3a+3b+2a-2b)(3a+3b-2a+2b)

=(5a+b)(a+5b);

(3)6xy2-9x2y-y3

=-y(y2-6xy+9x2

=-y(3x-y)2

(4)4+12(x-y)+9(x-y)2

=[3(x-y)+2]2

=(3x-3y+2)2

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