Question

Factor:$121m^2-1$.

Short answer

Factors of$121m^2-1$are$\left(11m-1\right)\left(11m+1\right)$.

Step-by-step solution

Step 1. Given information.

Given an expression$121m^2-1$.

Step 2. Find if the expression is of the form a2-b2.

Consider $a=11m,b=1$.

It can be seen that $121m^2-1={\left(11m\right)}^2-1^2$.

Therefore, the expression is of the form$a^2-b^2$.

Step 3. Write the product of conjugates.

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

It follows that$121m^2-1=\left(11m-1\right)\left(11m+1\right)$.

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl}\left(11m-1\right)\left(11m+1\right)& =& {\left(11m\right)}^2-1\\ & =& 121m^2-1\end{array}$