Question

(a+b) (a-b) (a²+ab+b²) (a²-ab+b²)

Answer 1

Solution:

(a+b)(a-b)(a²+ab+b²)(a²-ab+b²) =a⁶+b⁶+2(a²b⁴)

Explaination:

=a²-b²(a⁴-a³b+a²b²+a³b-a²b²+ab³+a²b²-ab³+b⁴)

=a²-b²[a⁴+b⁴(-a³b+a³b)+a²b²+(a²b²-a²b²)+(ab³-ab³)]

=a²-b²(a⁴+b⁴+a²b²)

=a⁶+a²b⁴+a⁴b²-a⁴b²+b⁶+a²b⁴

=a⁶+b⁶+(a²b⁴+a²b⁴)+(a⁴b²-a⁴b²)

=a⁶+b⁶+2(a²b⁴)