Q68. - Algebra 2

Question

Simplify. 

$\frac{\mathbf{1}}{\mathbf{3}}\left(\mathbf{15}\mathbf{a}+\mathbf{9}\mathbf{b}\right)-\frac{\mathbf{1}}{\mathbf{7}}\left(\mathbf{28}\mathbf{b}-\mathbf{84}\mathbf{a}\right)$

Step-by-Step Solution

Answer

The required simplified expression is $17a-b$.

Step 1 – State the concept

Simplifying an algebraic expression is nothing but reducing it to the simplest form such that there are no more like terms in the simplified expression.

Step 2 – List the given data

The given expression to be simplified is $\frac{1}{3}\left(15a+9b\right)-\frac{1}{7}\left(28b-84a\right)$

Step 3 – Simplify

$\frac{1}{3}\left(15a+9b\right)-\frac{1}{7}\left(28b-84a\right)$   (Given expression)

 

$\frac{1}{3}\left(15a\right)+\frac{1}{3}\left(9b\right)-\frac{1}{7}\left(28b\right)-\frac{1}{7}\left(-84a\right)$   (Distributive property)

 

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

 

$5a+3b-4b+12a$  (Simplify)

 

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

 

$\left(17a\right)+\left(-b\right)$  (Simplify)

 

$17a-b$   (Simplify)

 

So, $17a-b$ is the required simplified expression.