Question

How do you factor `9(x+4)^2+12(x+4)+4`?

Answer 1

`9(x+4)^2+12(x+4)+4 =color(blue)((3x+14)^2)`

Explanation:

You could expand each of the terms and then collect like terms before attempting to factor, but it is probably easier to temporarily substitute a variable for `(x+4)`; for example with `k=x+4` we would have:

`9k^2+12k+4`

which factors fairly easily into `(3k+2)^2`

then replacing the `k` with `x+4`
we get `(3(x+4)+2)^2=(3x+14)^2`