How do you factor #a^4-(b+c)^4# ?

1 Answer
George C.
Feb 23, 2018

#a^4-(b+c)^4 = (a-b-c)(a+b+c)(a^2 + b^2+2bc + c^2)#

Explanation:

Note that:

#A^2-B^2 = (A-B)(A+B)#

Hence we find:

#a^4-(b+c)^4 = (a^2)^2 - ((b+c)^2)^2#

#color(white)(a^4-(b+c)^4) = (a^2 - (b+c)^2)(a^2 + (b+c)^2)#

#color(white)(a^4-(b+c)^4) = (a - (b+c))(a + (b+c))(a^2 + (b+c)^2)#

#color(white)(a^4-(b+c)^4) = (a-b-c)(a+b+c)(a^2 + b^2+2bc + c^2)#

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