How do you factor $a^2+20a+64$ ?

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Answer 1 · 2015-06-08T19:56:12

$a^2+20a+64 = (a+4)(a+16)$

$(a+m)(a+n) = a^2+(m+n)a+(mxxn)$

So if we can find $m$ and $n$ with $m+n = 20$ and $mxxn = 64$ then we have our factorisation.

$64 = 2^6$ factors into the following pairs:

$1 xx 64$ , $2 xx 32$ , $4 xx 16$ , $8 xx 8$

It's easy to spot that the pair $4, 16$ will work.

How do you factor a^2+20a+64a^2+20a+64?