问题
计算题
将下列各式分解因式:
(1)x3﹣6x2+9x;
(2)2m2x2﹣18m2y2;
(3)(x2+y2)2﹣4x2y2.
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+y2)2﹣4x2y2,
=(x2+2xy+y2)(x2﹣2xy+y2),
=(x+y)2(x﹣y)2.