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Chapter 6: Q. 415 (page 636)

Recognize and Use the Appropriate Method to Factor a Polynomial Completely.

2b2-2bc+5cb-5c2

Short Answer

Expert verified

The factors of the given expression are(b-c)(2b+5c).

Step by step solution

01

Step 1. Given and explanation.

We have the equation 2b2-2bc+5cb-5c2.

We will solve and factor it out by grouping the like terms and then taking out the common factors.

02

Step 2. Grouping the like terms and taking common factors out.

We have 2b2-2bc+5cb-5c2.

=(2b2-2bc)+(5cb-5c2)

Taking out the common factors gives us

=2b(b-c)+5c(b-c)=(b-c)(2b+5c)

This shows that factors are(b-c)(2b+5c).

03

Step 3. Check the solution.

We will check the solution by simply multiplying the factors. If we get the given equation as the product, our answers are right.

So,

=(b-c)(2b+5c)=2b2+5cb-2bc-5c2

Thus our calculations are right.

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