# How do you simplify 1/3(15a+9b)-1/7(28b-84a)?

Jan 24, 2017

See the entire simplification process below

#### Explanation:

First, expand the terms in parenthesis by multiplying the by the terms outside their respective parenthesis:

$\textcolor{red}{\frac{1}{3}} \left(15 a + 9 b\right) - \textcolor{b l u e}{\frac{1}{7}} \left(28 b - 84 a\right) \to$

$\left(\textcolor{red}{\frac{1}{3}} \times 15 a\right) + \left(\textcolor{red}{\frac{1}{3}} \times 9 b\right) - \left(\textcolor{b l u e}{\frac{1}{7}} \times 28 b\right) + \left(\textcolor{b l u e}{\frac{1}{7}} \times 84 a\right) \to$

$5 a + 3 b - 4 b + 12 a$

Next, group like terms:

$5 a + 12 a + 3 b - 4 b$

Now. combine like terms:

$\left(5 + 12\right) a + \left(3 - 4\right) b$

$17 a - 1 b$

$17 a - b$