Q. 258 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$5m^{4}n+320m{n}^4$

Step-by-Step Solution

Answer

The required factors are $5mn(m+4n)(m^2-4mn+16n^2)$

Step 1. Given Information

The given expression is $5m^{4}n+320m{n}^4$

Step 2. Calculation

We will find the factors by taking common factor out from the expression and then use the trinomial pattern.

$$\begin{gathered} 5m^{4}n+320m{n}^4=5mn(m^3+64n^3) \\ =5mn(m^3+{\left(4n\right)}^3) \\ =5mn(m+4n)(m^2-4mn+16n^2) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 5mn(m+4n)(m^2-4mn+16n^2)=5mn(m^3+{\left(4n\right)}^3) \\ =5mn(m^3+64n^3) \\ =5m^{4}n+320m{n}^4 \end{gathered}$$