因式分解a^4b+a^3b^2-a^2b^3-ab^4
问题描述:
因式分解a^4b+a^3b^2-a^2b^3-ab^4
答
a^4 * b + a^3 * b^2 - a^2 * b^3 - a * b^4= a^3 * b(a + b) - a * b^3(a + b)= (a + b)(a^3 * b - a * b^3)= ab(a + b)(a^2 - b^2)= ab(a + b)(a + b)(a - b)= ab(a - b)(a + b)^2