Question

Rút gọn các biểu thức sau:

a) (a+b) (a\(^2\)\(-\)ab+b\(^2\)) + (a\(-\)b) (a\(^2\)+ab+b\(^2\))

b) (a+b) \([\)(a\(-\)b)\(^2\)+ab\(]\)

Answer 1

a.

\(\left(a+b\right)(a^2-ab+b^2)+\left(a-b\right)\left(a^2+ab+b^2\right)\)

= \(a^3+b^3+a^3-b^3\)

= \(2a^3\)

b.

\(\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)

= \(\left(a+b\right)\left[a^2-2ab+b^2+ab\right]\)

= \(\left(a+b\right)\left[a^2-ab+b^2\right]\)

= \(a^3+b^3\)

Answer 2

a.=(a³+b³)+(a³-b³)

=a³+b³+a³-b³

=2a³

Answer 3

b.ta có:(a+b)[(a-b)²+ab]

=(a+b)(a²-2ab+b²+ab)

=(a+b)(a²-ab+b²)

=a³+b³