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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 8: Q22. (page 514)

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

Short Answer

Expert verified

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

Step by step solution

01

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

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

$8 x y = 2 鈰� 2 鈰� 2 鈰� x 鈰� y 16 x^{3} y = 2 鈰� 2 鈰� 2 鈰� 2 鈰� x 鈰� x 鈰� x 鈰� y 10 y = 2 鈰� 5 鈰� y$

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 $2 鈰� y$ or $2 y$ .

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

02

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

Therefore, it is obtained that:

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

03

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:

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

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

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Most popular questions from this chapter

Use the Distributive Property to factor each polynomial.

$24 a m 鈭� 9 a n + 40 b m 鈭� 15 b n$

Solve each equation. Check your solution.

$2 x (x 鈭� 5) = 0$

A sidewalk of equal width is being built around a square yard. What is the width of the sidewalk?

A landscape architect is designing a stone path 36 inches wide and 120 inches long. What is the maximum size square stone that can be used so that none of the stones have to be cut?

Rewrite each expression using the Distributive Property. Then simplify.

$2 (3 + x)$

See all solutions

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