Q. 389 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible. 

$169m^2 - n^2$

Step-by-Step Solution

Answer

The Factored form of given polynomial is $(13m+n)(13m-n)$.

Step 1. Given Information

We are given a polynomial, 

$169m^2 - n^2$

The formula used for factoring using the difference of squares pattern is,

$a^2-b^2=(a+b)(a-b)$

Step 2. Factorizing the polynomial

The given polynomial can be written as, 

$169m^2 - n^2={\left(13m\right)}^2 - n^2$

Using $a^2-b^2=(a+b)(a-b)$, we get

$169m^2 - n^2=(13m+n)(13m-n)$

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get 

$$\begin{gathered} (13m+n)(13m-n)=169m^2 - n^2 \\ {\left(13m\right)}^2-13m\times n+n\times 13m-n^2=169m^2 - n^2 \\ 169m^2 - n^2=169m^2 - n^2 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.