Q. 392 - Intermediate Algebra

Question

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

$20x^2-125$

Step-by-Step Solution

Answer

The Factored form of given polynomial is,

$5(2x+5)(2x-5)$

Step 1. Given Information

We are given a polynomial,  

$20x^2-125$

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

Factoring out greatest common factor $5$, we get

$20x^2-125=5(4x^2-25)$

$20x^2-125=5({\left(2x\right)}^2-5^2)$

Using $a^2-b^2=(a+b)(a-b)$, we get

$20x^2-125=5(2x+5)(2x-5)$

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get 

$$\begin{gathered} 5(2x+5)(2x-5)=20x^2-125 \\ 5(4x^2-10x+10x-25)=20x^2-125 \\ 5(4x^2-25)=20x^2-125 \\ 20x^2-125=20x^2-125 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.