Q 179 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$6p^2{q}^2-54p^2$

Step-by-Step Solution

Answer

The complete factor of trinomial is $6p^2\left(q-3\right)\left(q+3\right)$.

Step 1. Given information

Consider the given trinomial.

$6p^2{q}^2-54p^2$

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.

$$\begin{gathered} 6p^2{q}^2-54p^2=6p^2\left(q^2-9\right) \\ =6p^2\left[{\left(q\right)}^2-{\left(3\right)}^2\right] \end{gathered}$$

Step 4. Write the trinomial as product of conjugate.

$6p^2\left[\left(q^2\right)-{\left(3\right)}^2\right]=6p^2\left(q-3\right)\left(q+3\right)$