Question

分解因式：?1、4a^2乘以b^2减(a^2+b^2)^2.?2、a的五次幂b-8a的立方乘以b的立方+16ab五次幂.

Answer 1

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

=(2ab)^2-(a^2+b^2)^2

=(2ab-a^2-b^2)(2ab+a^2+b^2)

=-(a-b)^2(a+b)^2.

a^5b-8a^3b^3+16ab^5

=ab(a^4-8a^2b^2+16b^4)

=ab(a^2-4b^2)^2

=ab(a-2b)^2(a+2b)^2.