Chapter A.2, Problem 87E

Solution

To factor completely $2ac-2bd+4ad-bc$ .

  $\left(2a-b\right)\left(c+2d\right)$

Given:

The expression, $2ac-2bd+4ad-bc$

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• In any expression, terms are separated by plus or minus signs.
• Coefficients are the constants in front of the variable terms.

Calculation:

In order to find the factor completely, first rearrange the equation and then factor out the common factor from each group and then solving it as shown below:

  $\begin{array}{l}2ac-2bd+4ad-bc\\ 2ac+4ad-bc-2bd\\ 2a\left(c+2d\right)-b\left(c+2b\right)\\ \left(2a-b\right)\left(c+2d\right)\end{array}$

The original expression now become

  $\left(2a-b\right)\left(c+2d\right)$