How do you factor #2d^4-32f^4#?

1 Answer
Dec 28, 2016

Answer:

#2d^4-32f^4 = 2(d-2f)(d+2f)(d^2+4f^2)#

Explanation:

The difference of squares identity can be written:

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

Hence we find:

#2d^4-32f^4 = 2(d^4-16f^4)#

#color(white)(2d^4-32f^4) = 2((d^2)^2-(4f^2)^2)#

#color(white)(2d^4-32f^4) = 2(d^2-4f^2)(d^2+4f^2)#

#color(white)(2d^4-32f^4) = 2(d^2-(2f)^2)(d^2+4f^2)#

#color(white)(2d^4-32f^4) = 2(d-2f)(d+2f)(d^2+4f^2)#

The remaining sum of squares can only be factored further with Complex coefficients.