Q. 6.83 - Intermediate Algebra

Question

Factor completely: $4p^{2}q-16pq+12q$

Step-by-Step Solution

Answer

The required factors are $4(p-3)(pq-q)$

Step 1. Given Information

The given expression is $4p^{2}q-16pq+12q$

Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis and then use the middle term splitting method.

$$\begin{gathered} 4p^{2}q-16pq+12q=4(p^{2}q-4pq+3q) \\ =4(p^{2}q-3pq-pq+3q) \\ =4\left[pq\right(p-3)-q(p-3\left)\right] \\ =4(p-3)(pq-q) \end{gathered}$$

Step 3. Check

We will verify by multiplying the factors.

$$\begin{gathered} 4(p-3)(pq-q)=4\left[pq\right(p-3)-q(p-3\left)\right] \\ =4(p^{2}q-3pq-pq+3q) \\ =4(p^{2}q-4pq+3q) \\ =4p^{2}q-16pq+12q \end{gathered}$$