How do you factor #x^4 – y^4#?

Question

120495 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-22T07:48:26

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

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)#

Answer 2 · 2018-07-22T09:08:36

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

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)#