# How do you combine like terms in 3( 2a - b ) - 7( 3b - 5a )?

May 13, 2018

$41 a - 5 b$

#### Explanation:

Before we combine like terms, we first use the distributive property, as shown here:

Following this image, we can distribute/expand $\textcolor{b l u e}{3 \left(2 a - b\right)}$ and $\textcolor{b l u e}{- 7 \left(3 b - 5 a\right)}$.

$\textcolor{b l u e}{3 \left(2 a - b\right) = 6 a - 3 b}$

$\textcolor{b l u e}{- 7 \left(3 b - 5 a\right) = - 21 b + 35 a}$

Now put these back into the expression:
$6 a - 3 b - 21 b + 35 a$

Now let's color-code the like terms:
$\textcolor{red}{6 a} \quad \textcolor{g r e e n}{- \quad 3 b} \quad \textcolor{g r e e n}{- \quad 2 b} \quad \textcolor{red}{+ \quad 35 a}$

Combine like terms:
$41 a - 5 b$

Hope this helps!