Q 185 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$169c^2-36d^2$

Step-by-Step Solution

Answer

The complete factor of trinomial is $\left(13c-6d\right)\left(13c+6d\right)$.

Step 1. Given information

Consider the given trinomial 

$169c^2-36d^2$

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.  

$169c^2-36d^2={\left(13c\right)}^2-{\left(6d\right)}^2$

Write them as product of conjugate.  

${\left(13c\right)}^2-{\left(6d\right)}^2=\left(13c-6d\right)\left(13c+6d\right)$