Q 186 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$36p^2-49q^2$

Step-by-Step Solution

Answer

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

Step 1. Given information

Consider the given trinomial

$36p^2-49q^2$

Step 2. Formula used

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

Step 3. Write the trinomial as squares.

Write the trinomial as perfect squared form. 

$36p^2-49q^2={\left(6p\right)}^2-{\left(7q\right)}^2$

Write them as product of conjugate.  

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