Factorize each of the following expressions:$x^6 +y^6$

Given:

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

$x^6 + y^6 = (x^2)^3 + (y^2)^3$

$= (x^2 + y^2) [(x^2)^2 - x^2 \times y^2 + (y^2)^2]$

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

Hence, $x^6 + y^6 = (x^2 + y^2) [x^4 - x^2y^2 + y^4]$.

Tutorialspoint

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started