Question

分解因式(a+b)^5-a^2-b^5

Answer 1

都是5次方吧

(a＋b)^5－a^5－b^5

=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5-a^5-b^5

=5a^4b+10a^3b^2+10a^2b^3+5ab^4

=5ab(a^3+2a^2b+2ab^2+b^3)

=5ab[(a^3+b^3)+2ab(a+b)]

=5ab[(a+b)(a^2-ab+b^2)+2ab(a+b)]

=5ab(a+b)(a^2-ab+b^2+2ab)

=5ab(a+b)(a^2+ab+b^2)