Question

The product (a + b) (a − b) (a² − ab + b²) (a² + ab + b²) is equal to

Options

• a⁶ + b⁶

• a⁶ − b⁶

•  a³ − b³

• a³ + b³

Answer 1

We have to find the product of  `(a+b)(a-b)(a^2 - ab +b^2)(a^2+ab +b^2)`

Using identity 

 `a^3 +b^3 = (a+b)(a^2 - ab+b^2 )`

 `a^3 -b^3 = (a-b)(a^2 +ab+b^2 )`

We can rearrange as 

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

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

Again using the identity  `(a+b)(a-b)= a^2 -b^2`

Here  `a = a^3,b = b^3`

`(a+b)(a-b) = a^2 - b^2`

                         ` = (a^3)^2 - (b^3)^2`

                           ` = a^6 - b^6`

Hence the product of   `(a+b)(a^2 - ab +b^2)(a-b)(a^2+ab +b^2)` is  `a^6 - b^6`.