Q14. - Algebra 1

Question

Factor each polynomial.

$2c^{2}d-4c^2{d}^2$

Step-by-Step Solution

Answer

A factor of given polynomial is $2c^{2}d\left(1-2d\right)$.

Step 1. Find GCF.

Find GCF of $2c^{2}d$ and $4c^2{d}^2$.

 

$$\begin{gathered} 2c^{2}d=2\cdot c\cdot c\cdot d \\ 4c^2{d}^2=2\cdot 2\cdot c\cdot c\cdot d\cdot d \end{gathered}$$

 

Therefore, GCF is $2c^{2}d$.

Step 2. Rewrite.

Rewrite each term using GCF.

$2c^{2}d-4c^2{d}^2=2c^{2}d\left(1\right)-2c^{2}d\left(2d\right)$

Step 3. Apply distributive property.

Apply distributive property, $a\left(b-c\right)=ab-ac$.

 

$2c^{2}d\left(1-2d\right)$

 

Therefore, factor of given polynomial is $2c^{2}d\left(1-2d\right)$.