Question

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

Answer 1

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

Explanation:

`(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.