How do you factor 8 - 2b - b^2?

Jun 18, 2015

 color(green)(-1(b-2)(b+4) is the factorised format.

Explanation:

$8 - 2 b - {b}^{2} = - \left({b}^{2} + 2 b - 8\right)$

We can Split the Middle Term of ${b}^{2} + 2 b - 8$ 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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 8 = - 8$
and
${N}_{1} + {N}_{2} = b = 2$
After trying out a few numbers we get ${N}_{1} = 4$ and ${N}_{2} = - 2$
$4 \cdot - 2 = - 8$ and $4 + \left(- 2\right) = 2$

${b}^{2} + 2 b - 8 = {b}^{2} + 4 b - 2 b - 8$
$= b \left(b + 4\right) - 2 \left(b + 4\right)$
$b + 4$ is common to both terms:
 =color(green)( (b-2)(b+4)