How do you factor $u^{2} - 16 v^{2}$ $u^2 - 16v^2$ ?

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Answer 1 · 2015-06-19T19:15:20

This is a difference of squares:

$u^{2} - 16 v^{2} = u^{2} - {(4 v)}^{2} = (u - 4 v) (u + 4 v)$ $u^2-16v^2 = u^2 - (4v)^2 = (u-4v)(u+4v)$

In general $a^{2} - b^{2} = (a - b) (a + b)$ $a^2 - b^2 = (a-b)(a+b)$

Putting $a = u$ $a=u$ and $b = 4 v$ $b=4v$ we have

$u^{2} - 16 v^{2} = u^{2} - {(4 v)}^{2}$ $u^2-16v^2 = u^2 - (4v)^2$

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

$= (u - 4 v) (u + 4 v)$ $= (u-4v)(u+4v)$

How do you factor u2−16v2u^2 - 16v^2?