Q 6.55 - Intermediate Algebra

Question

Factor: $196m^2-25n^2$.

Step-by-Step Solution

Answer

Factors of $196m^2-25n^2$ are $\left(14m-5n\right)\left(14m+5n\right)$.

Step 1. Given information.

Given an expression $196m^2-25n^2$.

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

Consider $a=14m,b=5n$.

It can be seen that $196m^2-25n^2=\left(14m-5n\right)\left(14m+5n\right)$.

Therefore, the expression is of the form .

Step 3. Write the product of conjugates.

Note that .

It follows that $196m^2-25n^2={\left(14m\right)}^2-{\left(5n\right)}^2$.

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl}\left(14m-5n\right)\left(14m+5n\right)& =& {\left(14m\right)}^2-{\left(5n\right)}^2\\ & =& 196m^2-25n^2\end{array}$