Q20. - Algebra 1

Question

Use the Distributive Property to factor each polynomial.

$12x+24y$

Step-by-Step Solution

Answer

The factorization of the given polynomial is $12\left(x+2y\right)$.

Step 1. Find the greatest common factor of 12 x and 24 y .

Find the factorization of $12x$ and $24y$.

$$\begin{gathered} 12x=2\cdot 2\cdot 3\cdot x \\ 24y=2\cdot 2\cdot 2\cdot 3\cdot y \end{gathered}$$ 

From the factorization of $12x$ and $24y$, it can be noticed that the greatest common factor of $12x$ and $24y$ is $2\cdot 2\cdot 3$ or 12.

Therefore, the greatest common factor of $12x$ and $24y$ is 12.

Step 2. Write each term as the product of the greatest common factor and the remaining factors.

Therefore, it is obtained that:

$12x+24y=12\left(x\right)+12\left(2y\right)$

Step 3. Use the distributive property to factor out the greatest common factor.

The distributive property states that:

$ab+ac=a\left(b+c\right)$

Now, use the distributive property to factor out the greatest common factor.

Therefore, it is obtained that:

$$\begin{gathered} 12x+24y=12\left(x\right)+12\left(2y\right) \\ =12\left(x+2y\right) \end{gathered}$$

Therefore, the factorization of the given polynomial is $12\left(x+2y\right)$.