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Chapter 7: Q 232. (page 867)

In the following exercises, factor.

90p3+300p2q+250pq2

Short Answer

Expert verified

The factorization of 90p3+300p2q+250pq2is,10p[(3p+5q)(3p+5q)].

Step by step solution

01

Step 1. Given information  

Given expression is90p3+300p2q+250pq2.

02

Step 2. Is there a GCF? 

Yes, 10p, so factor it out.

10p[9p2+30pq+25q2]

03

Step 3. Is this a perfect square trinomial? 

Verify the pattern.

a2+2ab+b2=10p[(3p)2-2(3p)(5q)+(5q)2]

04

Step 4. Factor 


10p(3p+5q)2=10p[(3p+5q)(3p+5q)]

05

Step 5. Check 

10p[(3p+5q)(3p+5q)]=10p(3p+5q)2=10p[(3p)2+2(3p)(5q)+(5q)2=10p[9p2+30pq+25q2]=90p3+300p2q+250pq2

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Most popular questions from this chapter

In the following exercises, factors completely:

3x2-75y2.

Factor:5x2-25x+15

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Solve:y-6y+9=0.

In the following exercises, solve.

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