How do you factor #4a^4 + b^4#?

1 Answer
Johnson Z.
Jun 6, 2016

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

Explanation:

Given,

#4a^4+b^4#

Rewrite each term such that both terms have an exponent of #2#.

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

Recall that the expression follows the sum of squares pattern, #color(red)(x^2)+color(blue)(y^2)=(color(red)xcolor(darkorange)+color(blue)ycolor(purple)i)(color(red)xcolor(darkorange)-color(blue)ycolor(purple)i)#. Thus,

#=color(green)(|bar(ul(color(white)(a/a)color(black)((2a^2+b^2i)(2a^2-b^2i))color(white)(a/a)|)))#

Related questions
See all questions in Factoring Completely
Impact of this question
8004 views around the world
You can reuse this answer
Creative Commons License