问2个数学的公式 (二项式定理)

<1>(a+b)^5 + (a-b)^5 =??? <2>(a+b) ^4 - (a-b)^4 =???
2025-12-24 09:17:41
推荐回答(1个)
回答1:

(a+b)^5 + (a-b)^5
=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5+
a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5
=2a^5+20a^3b^2+10ab^4.

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