Q. 388 - Intermediate Algebra

Question

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

$81r^2 - 25$

Step-by-Step Solution

Answer

The Factored form of given polynomial is $(9r-5)(9r+5)$.

Step 1. Given Information

We are given a polynomial, 

$81r^2 - 25$

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,

$81r^2-25=\left(9r\right)-5^2$

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

$81r^2-25=(9r-5)(9r+5)$

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

$$\begin{gathered} (9r-5)(9r+5)=81r^2-25 \\ {\left(9r\right)}^2+5\times 9r-5\times 9r-5^2=81r^2-25 \\ 81r^2-25=81r^2-25 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.