Q 6.56 - Intermediate Algebra

Question

Factor: $121p^2-9q^2$.

Step-by-Step Solution

Answer

Factors of $121p^2-9q^2$ are $\left(11p-3q\right)\left(11p+3q\right)$.

Step 1. Given information.

Given an expression $121p^2-9q^2$.

Step 2. Find if the expression is of the form a 2 - b 2 .

Consider $a=11p,b=3q$.

It can be seen that $121p^2-9q^2={\left(11p\right)}^2-{\left(3q\right)}^2$.

Therefore, the expression is of the form .

Step 3. Write the product of conjugates.

Note that .

It follows that $121p^2-9q^2=\left(11p-3q\right)\left(11p+3q\right)$.

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl}\left(11p-3q\right)\left(11p+3q\right)& =& {\left(11p\right)}^2-{\left(3q\right)}^2\\ & =& 121p^2-9q^2\end{array}$