问题 解答题

分解因式

(1)(a-b)(x-y)-(b-a)(x+y)

(2)ax2-4ax+4a

(3)(x2+1)2-4x2

(4)用简便方法计算:10032-9972

答案

(1)(a-b)(x-y)-(b-a)(x+y)

=(a-b)(x-y)+(a-b)(x+y)

=(a-b)(x-y+x+y)

=2x(a-b);

(2)ax2-4ax+4a

=a(x2-4x+4)

=a(x-2)2

(3)(x2+1)2-4x2

=(x2+2x+1)(x2-2x+1)

=(x+1)2(x-1)2

(4)10032-9972

=(1003+997)×

=2000×6

=12000.

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