Q. 391 - Intermediate Algebra

Question

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

$9-121y^2$

Step-by-Step Solution

Answer

The Factored form of given polynomial is,

$(3+11y)(3-11y)$

Step 1. Given Information

We are given a polynomial, 

$9-121y^2$

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,

$9-121y^2=3^2-{\left(11y\right)}^2$

Using $a^2-b^2=(a+b)(a-b)$, we get 

$9-121y^2=(3+11y)(3-11y)$

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get 

$$\begin{gathered} (3+11y)(3-11y)=9-121y^2 \\ {3}^2-3\times 11y+3\times 11y-{\left(11y\right)}^2=9-121y^2 \\ 9-121y^2=9-121y^2 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.