Question

How do you factor `a^2 + 12ab + 27b^2`?

Answer 1

`a^2+12ab+27b^2 = (a+3b)(a+9b)`

Explanation:

The key is to recognize that
`color(white)("XXXX")` `3xx9 = 27`
and
`color(white)("XXXX")` `3+9 = 12`

Since `(a+pb)(a+qb) = a^2 + (p+q)ab + (pq)b^2`
and the given expression has
`color(white)("XXXX")` `(p+q) = 12`
and
`color(white)("XXXX")` `(pq) = 27`