问题 计算题

将下列各式分解因式:

(1)x3﹣6x2+9x;

(2)2m2x2﹣18m2y2

(3)(x2+y22﹣4x2y2

答案

解:(1)x3﹣6x2+9x,

=x(x2﹣6x+9),

=x(x﹣3)2

(2)2m2x2﹣18m2y2

=2m2(x2﹣9y2),

=2m2(x+3y)(x﹣3y);

(3)(x2+y22﹣4x2y2

=(x2+2xy+y2)(x2﹣2xy+y2),

=(x+y)2(x﹣y)2

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