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

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Answer 1 · 2017-01-19T22:41:29

$np+2n+8p+16 = (n+8)(p+2)$

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:

$np+2n+8p+16 = (np+2n)+(8p+16)$

$color(white)(np+2n+8p+16) = n(p+2)+8(p+2)$

$color(white)(np+2n+8p+16) = (n+8)(p+2)$

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