# How do you factor 15ab-12+18a-10b?

May 24, 2017

$\left(3 a - 2\right) \left(5 b + 6\right)$

#### Explanation:

Let:

$P \left(x\right) = 15 a b - 12 + 18 a - 10 b$

First we note that there are two terms that contain $a$, so gather these terms up and factor out $a$:

$P \left(x\right) = 15 a b + 18 a - 12 - 10 b$
$\text{ } = a \left(15 b + 18\right) - 12 - 10 b$

The term in brackets also has a common factor of $3$, so:

$P \left(x\right) = a \left(3 \left(5 b + 6\right)\right) - 12 - 10 b$
$\text{ } = 3 a \left(5 b + 6\right) - 12 - 10 b$

And for the second terms we have a common factor of $3$,so:

$P \left(x\right) = 3 a \left(5 b + 6\right) + 2 \left(- 6 - 5 b\right)$

We can also factorise $- 1$ from the second term to get:

$P \left(x\right) = 3 a \left(5 b + 6\right) - 2 \left(6 + 5 b\right)$
$\text{ } = 3 a \left(5 b + 6\right) - 2 \left(5 b + 6\right)$

Finally, we now have two terms with a common factor of $\left(5 b + 6\right)$ so:

$P \left(x\right) = \left(3 a - 2\right) \left(5 b + 6\right)$