Question

4a²b²-（a²+b²）²和a的5次方-8a的3次方b的3次方+16ab的5次方 分解因式

Answer 1

=4a^2b^2-a^4-b^4-2a^2b^2

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

Answer 2

4a²b²-（a²+b²）²
=(2ab)²-(a²+b²)²
=[2ab+(a²+b²)][2ab-(a²+b²)]
=(a²+2ab+b²)[-(a²-2ab+b²)]
=-(a+b)²(a-b)²
=-[(a+b)(a-b)]²
=-(a²-b²)²

a^5b-8a³b³+16ab^5
=ab(a^4-8a²b²+16b^4)
=ab(a²-4b²)
=ab(a+2b)(a-2b)