How do you factor #2x^4-32y^4#?

1 Answer
Sep 2, 2016

Answer:

#2x^4-32y^4 = 2(x-2y)(x+2y)(x^2+4y^2)#

Explanation:

The difference of squares identity can be written:

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

Hence we find:

#2x^4-32y^4 = 2(x^4-16y^4)#

#color(white)(2x^4-32y^4) = 2((x^2)^2-(4y^2)^2)#

#color(white)(2x^4-32y^4) = 2(x^2-4y^2)(x^2+4y^2)#

#color(white)(2x^4-32y^4) = 2(x^2-(2y)^2)(x^2+4y^2)#

#color(white)(2x^4-32y^4) = 2(x-2y)(x+2y)(x^2+4y^2)#