Question

乘法公式的推广(a-b)(a+b)=a2-b2(a-b)(a2+ab+b2)=a5-b5那么a4-b4a5-b5an-b

Answer 1

a^4-b^4=(a-b)(a^3+a^2b+ab^2+b^3),

a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4),

a^n-b^n=(a-b)[a^(n-1)+a^(n-2)b+a^(n-3)b^2+...+ab^(n-2)+b^(n-1)].