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Chapter 7: Q 226. (page 867)

In the following exercises, factor.

100y2-20y+1

Short Answer

Expert verified

The factorization of100y2-20y+1is,(10y-1)(10y-1).

Step by step solution

01

Step 1. Given information

Given expression is100y2-20y+1.

02

Step 2. Write it as a square.

(a)2=(10y)2(b)2=(1)2

Check the middle term. Is it 2ab?

role="math" localid="1649797234527" 2ab=(2)(10y)(1)=20y

Yes, the middle term is equal to2ab.

03

Step 3. Write the square of the binomial.

100y2-20y+1=(10y-1)2=(10y-1)(10y-1)

04

Step 4. Check by multiplying

(10y-1)(10y-1)=(10y-1)2=(10y)2-(2)(10y)(1)+(1)2=(10y)2-20y+(1)2

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