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

1 Answer
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)|)))