# How do you factor completely: 8x^2 - 8x - 16?

##### 1 Answer
Jul 17, 2015

color(blue)(8(x+1)(x−2)

#### Explanation:

8x^2−8x−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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 8 \cdot \left(- 16\right) = - 128$
and
${N}_{1} + {N}_{2} = b = - 8$

After trying out a few numbers we get ${N}_{1} = - 16$ and ${N}_{2} = 8$

$\left(- 16\right) \cdot 8 = - 128$, and $- 16 + 8 = - 8$

8x^2−color(blue)(8x)−16 = 8x^2−color(blue)(16x +8x)−16

= 8x(x−2) +8(x−2)

$= \left(8 x + 8\right) \left(x - 2\right)$

= color(blue)(8(x+1)(x−2)  ,which is the factorised form.