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Chapter 7: Q 231. (page 867)

In the following exercises, factor.

75u3-3u2v+3uv2

Short Answer

Expert verified

The factorization of 75u3-3u2v+3uv2is,3u[(5u-v)(5u-v)].

Step by step solution

01

Step 1. Given information  

Given expression is75u3-3u2v+3uv2.

02

Step 2. Is there a GCF? 

Yes, 3u, so factor it out.

3u(25u2-10uv+v2)

03

Step 3. Is this a perfect square trinomial?

Verify the pattern.

a2-2ab+b2=3u[(5u)2-2(5u)(v)+(v)2]

04

Step 4. Factor

3u[5u-v]2=3u[(5u-v)(5u-v)]

05

Step 5. Check

3u[(5u-v)(5u-v)]=3u(5u-v)2=3u[(5u)2-2(5u)(v)+(v)2]=3u[25u2-10uv+v2]=75u3-30u2v+3uv2

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