Chapter 8: Q20. (page 514)

Use the Distributive Property to factor each polynomial.
$12 x + 24 y$

Short Answer

Expert verified

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

Step by step solution

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

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

localid="1647527640236" $12 x = 2 \cdot 2 \cdot 3 \cdot x 24 y = 2 \cdot 2 \cdot 2 \cdot 3 \cdot y$

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

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

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

Therefore, it is obtained that:

$12 x + 24 y = 12 (x) + 12 (2 y)$

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

The distributive property states that:

$a b + a c = a (b + c)$

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

Therefore, it is obtained that:

$12 x + 24 y = 12 (x) + 12 (2 y) = 12 (x + 2 y)$

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

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Use the Distributive Property to factor each polynomial.
$12 x + 24 y$

Short Answer

Step by step solution

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

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

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

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Use the Distributive Property to factor each polynomial.12x+24y

Short Answer

Step by step solution

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Use the Distributive Property to factor each polynomial.
$12 x + 24 y$