Q. 247 - Intermediate Algebra

Question

In the following exercises, factor completely.   

$3x^{4}y-81xy$

Step-by-Step Solution

Answer

The required factors are $3xy(x-3)(x^2+3x+9)$

Step 1. Given Information

The given expression is $3x^{4}y-81xy$

Step 2. Calculation

We will find the factors by factoring out the common term and then apply the property,

$$\begin{gathered} 3x^{4}y-81xy=3xy(x^3-27) \\ =3xy(x^3-3^3) \\ =3xy(x-3)(x^2+3x+9) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 3xy(x-3)(x^2+3x+9)=3xy(x^3-3^3) \\ =3xy(x^3-27) \\ =3x^{4}y-81xy \end{gathered}$$