Q. 6.78 - Intermediate Algebra

Question

Factor completely: $2p^3+54q^3$

Step-by-Step Solution

Answer

The required factors are $2(p+3q)(p^2-3pq+9q^2)$

Step 1. Given Information

The given expression is $2p^3+54q^3$

Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis and then apply the property.

$$\begin{gathered} 2p^3+54q^3=2(p^3+27q^3) \\ =2(p^3+{\left(3q\right)}^3) \\ =2(p+3q)(p^2-3pq+9q^2) \end{gathered}$$

Step 3. Check

We will verify by multiplying the factors.

$$\begin{gathered} 2(p+3q)(p^2-3pq+9q^2)=2(p^3+{\left(3q\right)}^3) \\ =2(p^3+27q^3) \\ =2p^3+54q^3 \end{gathered}$$