# How do you factor m^2+6m-27=0?

Sep 20, 2015

color(blue)((m-3)(m+9)  is the factorised form of the expression.

#### Explanation:

${m}^{2} + 6 m - 27 = 0$

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 27 = - 27$

AND

${N}_{1} + {N}_{2} = b = 6$

After trying out a few numbers we get ${N}_{1} = - 3$ and ${N}_{2} = 9$
$\left(9\right) \cdot \left(- 3\right) = - 27$ and $9 + \left(- 3\right) = 6$

${m}^{2} + 6 m - 27 = {m}^{2} - 3 m + 9 m - 27$

$= m \left(m - 3\right) + 9 \left(m - 3\right)$

color(blue)((m-3)(m+9)  is the factorised form of the expression.