How do you factor $4 a^{4} + b^{4}$ $4a^4 + b^4$ ?

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How do you factor $4 a^{4} + b^{4}$ $4a^4 + b^4$ ?

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Answer 1 · 2016-06-06T00:22:16

$4 a^{4} + b^{4} = (2 a^{2} + b^{2} i) (2 a^{2} - b^{2} i)$ $4a^4+b^4=(2a^2+b^2i)(2a^2-b^2i)$

Explanation:

Given,

$4 a^{4} + b^{4}$ $4a^4+b^4$

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

$= {(2 a^{2})}^{2} + {(b^{2})}^{2}$ $=(2a^2)^2+(b^2)^2$

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

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

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How do you factor $4 a^{4} + b^{4}$ $4a^4 + b^4$ ?

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