Question

(x − y) (x + y) (x² + y²) (x⁴ + y⁴) is equal to ______.

Options

• x¹⁶ − y¹⁶

• x⁸ − y⁸

•  x⁸ + y⁸

• x¹⁶ + y¹⁶

Answer 1

(x − y) (x + y) (x² + y²) (x⁴ + y⁴) is equal to x⁸ − y⁸.

Explanation:

Given  `(x-y)(x+y)(x^2 +y^2)(x^4 + y^4)`

Using the identity  `(x-y) (x+y) = x^2 - y^2`

`(x-y)(x+y)(x^2 +y^2)(x^4 + y^4) =  (x-y)(x+y)(x^2 +y^2)(x^4 + y^4)`

` = (x^2-y^2)(x^2 + y^2)(x^4 + y^4)`

`= [(x^2)^2 - (y^2)^2][x^4 +y^4]`

` = [(x^4)^2 - (y^4)^2]`

` = [x^8 - y^8]`

Hence `(x-y)(x+y)(x^2 +y^2)(x^4 + y^4)` is equal to ` x^8 - y^8`.