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Chapter 6: Q. 392 (page 635)

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

20x2鈭�125

Short Answer

Expert verified

The Factored form of given polynomial is,

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

Step by step solution

01

Step 1. Given Information 

We are given a polynomial,

20x2鈭�125

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

a2-b2=(a+b)(a-b)

02

Step 2. Factorizing the polynomial 

Factoring out greatest common factor 5, we get

20x2鈭�125=5(4x2-25)

20x2鈭�125=5(2x2-52)

Usinga2-b2=(a+b)(a-b), we get

20x2鈭�125=5(2x+5)(2x-5)

03

Step 3. Checking the factorization by multiplying 

Multiplying the factors, we get

5(2x+5)(2x-5)=20x2鈭�1255(4x2-10x+10x-25)=20x2鈭�1255(4x2-25)=20x2鈭�12520x2鈭�125=20x2鈭�125LHS=RHS

Hence the factorization is correct.

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