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Chapter 7: Q. 7.124 (page 872)

Factor completely:

27y2-48

Short Answer

Expert verified

The factored form is 3(3y+4)(3y-4).

Step by step solution

01

Step 1. Given Information 

We are given a polynomial 27y2-48,

We have to factor the given polynomial.

02

Step 2. Factoring the polynomial 

Factoring out GCF 3, we get

role="math" localid="1647769676037" 27y2-48=39y2-1627y2-48=33y2-42

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

27y2-48=3(3y+4)(3y-4)

03

Step 3. Checking the factors 

Multiplying the factors, we get

3(3y+4)(3y-4)=27y2-483(9y2-16)=27y2-4827y2-48=27y2-48LHS=RHS

Hence, the factors are correct.

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