Q. 253 - Intermediate Algebra

Question

In the following exercises, factor completely.    

$15pq-15p+12q-12$

Step-by-Step Solution

Answer

The required factors are $(15p+12)(q-1)$

Step 1. Given Information

The given expression is $15pq-15p+12q-12$

Step 2. Calculation

We will find the factors by grouping the terms with common factors and then factor out the common factors from each group.

$$\begin{gathered} 15pq-15p+12q-12=(15pq-15p)+(12q-12) \\ =15p(q-1)+12(q-1) \\ =(15p+12)(q-1) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (15p+12)(q-1)=15p(q-1)+12(q-1) \\ =(15pq-15p)+(12q-12) \\ =15pq-15p+12q-12 \end{gathered}$$