Q. 415 - Intermediate Algebra

Question

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

$2b^2-2bc+5cb-5c^2$

Step-by-Step Solution

Answer

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

Step 1. Given and explanation.

We have the equation $2b^2-2bc+5cb-5c^2$.

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

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

We have $2b^2-2bc+5cb-5c^2$.

$=(2b^2-2bc)+(5cb-5c^2)$

Taking out the common factors gives us

$$\begin{gathered} =2b(b-c)+5c(b-c) \\ =(b-c)(2b+5c) \end{gathered}$$

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

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,

$$\begin{gathered} =(b-c)(2b+5c) \\ =2b^2+5cb-2bc-5c^2 \end{gathered}$$

Thus our calculations are right.