Q. 262 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$3v^4-768$

Step-by-Step Solution

Answer

The required factors are $3(v^2+16)(v+4)(v-4)$

Step 1. Given Information

The given expression is $3v^4-768$

Step 2. Calculation

We will find the factors by taking common factor out from the expression and then use the difference of square patterns.

$$\begin{gathered} 3v^4-768=3(v^4-256) \\ =3({\left(v^2\right)}^2-{\left(16\right)}^2) \\ =3(v^2+16)(v^2-16) \\ =3(v^2+16)(v^2-4^2) \\ =3(v^2+16)(v+4)(v-4) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 3(v^2+16)(v+4)(v-4)=3(v^2+16)(v^2-4^2) \\ =3(v^2+16)(v^2-16) \\ =3({\left(v^2\right)}^2-{\left(16\right)}^2) \\ =3(v^4-256) \\ =3v^4-768 \end{gathered}$$