Chapter 8: Q22. (page 514)

Use the Distributive Property to factor each polynomial.
$8 x y - 16 x^{3} y + 10 y$

Short Answer

Expert verified

The factorization of the given polynomial is $2 y (4 x - 8 x^{3} + 5)$

Step by step solution

Step 1. Find the greatest common factor of 8xy,16x3y and 10y.

Find the factorization of $8 x y, 16 x^{3} y$ and $10 y$ .

$8 x y = 2 \cdot 2 \cdot 2 \cdot x \cdot y 16 x^{3} y = 2 \cdot 2 \cdot 2 \cdot 2 \cdot x \cdot x \cdot x \cdot y 10 y = 2 \cdot 5 \cdot y$

From the factorization of $8 x y, 16 x^{3} y$ and $10 y$ , it can be noticed that the greatest common factor of $8 x y, 16 x^{3} y$ and $10 y$ is $2 \cdot y$ or $2 y$ .

Therefore, the greatest common factor of $8 x y, 16 x^{3} y$ and $10 y$ is $2 y$ .

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

Therefore, it is obtained that:

$8 x y - 16 x^{3} y + 10 y = 2 y (4 x) - 2 y (8 x^{3}) + 2 y (5)$

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:

$8 x y - 16 x^{3} y + 10 y = 2 y (4 x) - 2 y (8 x^{3}) + 2 y (5) = 2 y (4 x - 8 x^{3} + 5)$

Therefore, the factorization of the given polynomial is $2 y (4 x - 8 x^{3} + 5)$ .

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Use the Distributive Property to factor each polynomial.
$8 x y - 16 x^{3} y + 10 y$

Short Answer

Step by step solution

Step 1. Find the greatest common factor of 8xy,16x3y and 10y.

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.8xy−16x3y+10y

Short Answer

Step by step solution

Step 1. Find the greatest common factor of 8xy,16x3y and 10y.

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

Logic and Functions

Statistics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the Distributive Property to factor each polynomial.
$8 x y - 16 x^{3} y + 10 y$