多项式化因式分解,因式分解(a^5+b^5)-(a^3b^2+a^2b^3)=?

Question

多项式化因式分解,
因式分解
(a^5+b^5)-(a^3b^2+a^2b^3)=?

Answer 1

【立方差公式：a^3-b^3=(a-b)(a^2+ab+b^2)】
(a^5+b^5)-(a^3b^2+a^2b^3)
= a^5-a^3b^2+b^5-a^2b^3
= a^3(a^2-b^2)+b^3(b^2-a^2)
= a^3(a^2-b^2)-b^3(a^2-b^2)
= (a^3-b^3)(a^2-b^2)
= (a-b)(a^2+ab+b^2)(a+b)(a-b)
= (a+b)(a-b)^2(a^2+ab+b^2)