Question

Is it possible to factor `y=x^2 +8x +16`? If so, what are the factors?

Answer 1

`x^2+8x+16 = (x+4)^2`

Explanation:

This is a perfect square trinomial.

First notice that both `x^2` and `16 = 4^2` are perfect squares.

Then multiply out `(x+4)^2` (using FOIL if you find it helpful) to see if the middle term matches:

`(x+4)^2`

`= (x+4)(x+4)`

`= stackrel "First" overbrace((x*x)) + stackrel "Outside" overbrace((x * 4)) + stackrel "Inside" overbrace((4 * x)) + stackrel "Last" overbrace((4*4))`

`=x^2+4x+4x+16`

`=x^2+8x+16`

In general note that `(a+b)^2 = a^2+2ab+b^2`, so if you recognise `a` and `b` then just check that the middle term is `2ab`.