Q 180 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$98r^3-72r$

Step-by-Step Solution

Answer

The complete factor of trinomial is $2r\left(7r-6\right)\left(7r+6\right)$.

Step 1. Given information

Consider the given trinomial.

$98r^3-72r$

Step 2. Formula used

$a^2-b^2=\left(a+b\right)\left(a-b\right)$

Step 3. Find the factor using difference of square pattern.

$$\begin{gathered} 98r^3-72r=2r\left(49r^2-36\right) \\ =2r\left({\left(7r\right)}^2-6^2\right) \end{gathered}$$

Step 4. Write the trinomial as product of conjugate.

$2r\left({\left(7r\right)}^2-6^2\right)=2r\left(7r-6\right)\left(7r+6\right)$