How do you factor x^4 – y^4?

2 Answers
Jul 22, 2018

(x+y)(x-y)(x^2+y^2)

Explanation:

Expression =x^4-y^4

Recall the factorization of the difference of two squares:

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

In our example, we will use this factorization twice.

Note: x^4 =(x^2)^2 and y^4 =(y^2)^2

Applying the factorization above:

Expression = (x^2+y^2)(x^2-y^2)

Now, the second factor above is also the difference of two squares.

Hence, Expression =(x+y)(x-y)(x^2+y^2)

(x-y)(x+y)(x^2+y^2)

Explanation:

Given that

x^4-y^4

=(x^2)^2-(y^2)^2

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

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