# How do you factor 4x^2+16x+16?

May 17, 2015

$4 {x}^{2} + 16 x + 16$

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:

${N}_{1} \cdot {N}_{2} = a \times c = 4 \times 16 = 64$
and
${N}_{1} + {N}_{2} = b = 16$

After trying out a few numbers we get ${N}_{1} = 8$ and ${N}_{2} = 8$
$8 \times 8 = 64$, and $8 + 8 = 16$

$4 {x}^{2} + 16 x + 16 = 4 {x}^{2} + 8 x + 8 x + 16$
$= 4 x \left(x + 2\right) + 8 \left(x + 2\right)$
$= \left(4 x + 8\right) \left(x + 2\right)$
The factor 4 is common to the terms in the first group above
$= \left\{4 \left(x + 2\right)\right\} \left(x + 2\right)$
$= \textcolor{g r e e n}{\left\{4 \left(x + 2\right)\right\} \left(x + 2\right)}$ is the Factorised form of $4 {x}^{2} + 16 x + 16$