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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 7: Q18. (page 463)

Find each product.
$(2 a - 5) (3 a + 5)$

Short Answer

Expert verified

The product of $(2 a - 5) (3 a + 5)$ is $6 a^{2} - 5 a - 25$ .

Step by step solution

01

Step 1. Write distributive property.

For any numbers, $a, b$ and c, $a (b + c) = a b + a c$ .

02

Step 2. Apply distributive property.

Apply distributive property to the given expression.

$2 a (3 a + 5) - 5 (3 a + 5) = 2 a \cdot 3 a + 2 a \cdot 5 - 5 \cdot 3 a - 5 \cdot 5$

03

Step 3. Multiply and simplify.

Multiply terms in the above expression and simplify it further.

$6 a^{2} + 10 a - 15 a - 25 = 6 a^{2} - 5 a - 25$

Therefore, the product of $(2 a - 5) (3 a + 5)$ is $6 a^{2} - 5 a - 25$ .

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Most popular questions from this chapter

Express each number in standard form.

$9.1 \times 10^{6}$

PACKAGING For a commercial art class, Aiko must design a new container for individually wrapped pieces of candy. The shape that she chose is a cylinder. The formula for the volume of a cylinder is $V = π r^{2} h$ .

a. The radius that Aiko would like to use is $2 p^{3}$ , and the height is $4 p^{3}$ . Write a monomial that represents the volume of her container.

b. Make a table of values for five possible radius widths and heights if the volume is to remain the same.

c. What is the volume of Aiko’s container if the height is doubled?

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

122

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$3 a^{4}$

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$2 c + 2$

See all solutions

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