How do you factor np+2n+8p+16?

Jan 19, 2017

$n p + 2 n + 8 p + 16 = \left(n + 8\right) \left(p + 2\right)$

Explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms.

So this quadrinomial will factor by grouping:

$n p + 2 n + 8 p + 16 = \left(n p + 2 n\right) + \left(8 p + 16\right)$

$\textcolor{w h i t e}{n p + 2 n + 8 p + 16} = n \left(p + 2\right) + 8 \left(p + 2\right)$

$\textcolor{w h i t e}{n p + 2 n + 8 p + 16} = \left(n + 8\right) \left(p + 2\right)$