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

Jun 8, 2015

${a}^{2} + 20 a + 64 = \left(a + 4\right) \left(a + 16\right)$

#### Explanation:

$\left(a + m\right) \left(a + n\right) = {a}^{2} + \left(m + n\right) a + \left(m \times n\right)$

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

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

$1 \times 64$, $2 \times 32$, $4 \times 16$, $8 \times 8$

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