# How do you write  x^2 + 8x + 16  in factored form?

Sep 16, 2015

color(blue)((x+4)(x+4)

#### Explanation:

${x}^{2} + 8 x + 16$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 4 \cdot 4 = 16$
and
${N}_{1} + {N}_{2} = b = 8$

After trying out a few numbers we get ${N}_{1} = 4$ and ${N}_{2} = 4$
$4 \cdot 4 = 16$ and $4 + 4 = 8$

${x}^{2} + 8 x + 16 = {x}^{2} + 4 x + 4 x + 16$
$= x \left(x + 4\right) + 4 \left(x + 4\right)$

color(blue)((x+4)(x+4)