Question

(a+b)的三次方+(a-b)的三次方 和 (a+b)的三次方-(a-b)的三次方 怎么做？要过程谢谢。

Answer 1

原式=a³+3a²b+3ab²+b³+a³-3a²b+3ab²-b³
=2a³+6ab²

原式=a³+3a²b+3ab²+b³-a³+3a²b-3ab²+b³
=6a²b+2b³

Answer 2

也可以这样
1 x^3+y^3=(x+y)(x^2-xy+y^2)

(a+b)^3+(a-b)^3
=[(a+b)+(a-b)][(a+b)^2-(a+b)(a-b)+(a-b)^2]
=2a(2a^2+2b^2+b^2-a^2)
=2a(a^2+3b^2)
=2a^3+6ab^2

2 x^3-y^3=(x-y)(x^2+xy+y^2)

(a+b)^3-(a-b)^3
=[(a+b)-(a-b)][(a+b)^2+(a+b)(a-b)+(a-b)^2]
=2b(2a^2+2b^2+a^2-b^2)
=6a^2b+2b^3