/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 Multiply. $$ 8(3 x+5 y) $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 53

Multiply. $$ 8(3 x+5 y) $$

Short Answer

Expert verified
24x + 40y

Step by step solution

01

- Distribute the Multiplication

Apply the distributive property of multiplication to expand the expression. You need to multiply each term inside the parentheses by the factor outside. In this case, multiply 8 by both terms inside the parentheses, which are 3x and 5y.
02

- Multiply Each Term

First, multiply 8 by 3x: \[ 8 \times 3x = 24x \]Second, multiply 8 by 5y: \[ 8 \times 5y = 40y \]
03

- Combine the Products

Combine the results from Step 2 to form the expanded expression. The expanded form will be the sum of the products:\[ 24x + 40y \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplication
Multiplication is one of the four basic mathematical operations. It involves finding the total number of objects in a given number of equal-sized groups. In the context of our exercise, we use multiplication to scale up the values of algebraic terms. For example, to multiply 8 by 3x:

\[ 8 \times 3x = 24x \]

This means 3x is added together 8 times, resulting in 24x. Similarly, 8 multiplied by 5y becomes 40y.
algebraic expressions
Algebraic expressions are mathematical phrases that include numbers, variables, and operations. In the given exercise, we have the expression \[ 8(3x + 5y) \]

Here, 3x and 5y are algebraic terms. The expression inside the parentheses is called a binomial because it contains two terms. To work with algebraic expressions, you follow the same arithmetic operations as you would with regular numbers, including addition, subtraction, multiplication, and division.
expanding expressions
Expanding expressions means simplifying an expression by removing parentheses. You do this by using the distributive property of multiplication over addition or subtraction. In our exercise, to expand \[ 8(3x + 5y) \]

You distribute 8 to both 3x and 5y:
  • First, multiply 8 by 3x to get 24x.
  • Then, multiply 8 by 5y to get 40y.

Finally, you combine the terms to get the expanded form:

\[ 24x + 40y \]
mathematical operations
Mathematical operations include addition, subtraction, multiplication, and division. These operations follow specific rules known as the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

In our exercise, we primarily use multiplication to expand the expression. Understanding how to apply these operations correctly is crucial for solving algebraic expressions and other math problems effectively.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Translate to an inequality. A number \(x\) is nonpositive.

List in order from least to greatest. $$-\frac{2}{3}, \frac{1}{2},-\frac{3}{4},-\frac{5}{6}, \frac{3}{8}, \frac{1}{6}$$

Simplify. Match the algebraic expression with the equivalent rewritten expression below. Check your answer by calculating the expression by hand and by using a calculator. A) \((5(3-7)+4 \wedge 3) /(-2-3)^{2}\) B) \((5(3-7)+4 \wedge 3) /\left(-2-3^{2}\right)\) C)\((5(3-7)+4) \wedge 3 /-2-3^{2}\) D) \(5(3-7)+4 \wedge 3 /(-2-3)^{2}\) $$ \frac{5(3-7)+4^{3}}{(-2-3)^{2}} $$

The deepest point in the Pacific Ocean is the Challenger Deep in the Marianas Trench, with a depth of \(10,911.5 \mathrm{m}\). The deepest point in the Atlantic Ocean is the Milwaukee Deep in the Puerto Rico Trench, with a depth of \(8530 \mathrm{m} .\) What is the difference in elevation of the two trenches?

Simplify. $$ |10(-5)|+1(-1) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.