Q. 6.77 - Intermediate Algebra

Question

Factor completely: $250m^3+432n^3$

Step-by-Step Solution

Answer

The required factors are $2(5m+6n)(25m^2-30mn+36n^2)$

Step 1. Given Information

The given expression is $250m^3+432n^3$

Step 2. Calculation

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

$$\begin{gathered} 250m^3+432n^3=2(125m^3+216n^3) \\ =2({\left(5m\right)}^3+{\left(6n\right)}^3) \\ =2(5m+6n)(25m^2-30mn+36n^2) \end{gathered}$$

Step 3. Check

We will verify by multiplying the factors.

$$\begin{gathered} 2(5m+6n)(25m^2-30mn+36n^2)=2({\left(5m\right)}^3+{\left(6n\right)}^3) \\ =2(125m^3+216n^3) \\ =250m^3+432n^3 \end{gathered}$$