/*! 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 209 Multiply. $$4(x+10)$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 209

Multiply. $$4(x+10)$$

Short Answer

Expert verified
4x + 40

Step by step solution

01

- Distribute 4 to each term inside the parentheses

Multiply the constant 4 by each term inside the parentheses separately. This means multiplying 4 by the variable term x and then by the constant term 10.
02

- Multiply 4 by x

When you multiply 4 by x, you get: \(4 \times x = 4x\)
03

- Multiply 4 by 10

When you multiply 4 by 10, you get: \(4 \times 10 = 40\)
04

- Combine the results

Add the two products obtained from the previous steps. Thus, the expression becomes: \(4x + 40\)

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.

Algebraic Multiplication
Algebraic multiplication is a fundamental concept in elementary algebra. It involves multiplying constants, variables, or combinations of both. In this exercise, we start by using the distributive property to multiply a constant across terms inside parentheses. The distributive property states that:
\[a(b + c) = ab + ac\]
This means we multiply the constant outside the parentheses by each term inside the parentheses. For example, for the expression
\[4(x + 10)\],
we distribute the 4 to both x and 10.
Combine Like Terms
Combining like terms is a key part of simplifying algebraic expressions. Terms are 'like' if they have the same variable raised to the same power. For instance, in the given problem, after using the distributive property, we have:
\[4x + 40\]
Here, 4x and 40 are our terms. Since there's no other x term or constant term to combine with, the expression is already simplified. But if there were similar terms like 4x + 3x, we would add them to get 7x.
Elementary Algebra
Elementary algebra introduces the basic building blocks for more advanced mathematics. This includes understanding how to work with variables, constants, and operations like addition, subtraction, multiplication, and division. In this exercise, we focused on the distributive property and combining like terms.
By mastering these basics, students can tackle more complex algebraic problems with confidence. The expression we worked on,
\[4(x + 10)\],
allowed us to see how constants and variables interact through multiplication and simplification.

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

Divide each polynomial by the monomial. $$\left(63 m^{4}-42 m^{3}\right) \div\left(-7 m^{2}\right)$$

Divide each polynomial by the monomial. $$\frac{51 m^{4}+72 m^{3}}{-3}$$

Mixed Practice $$\frac{32 c^{11}}{4 c^{5}}+\frac{42 c^{9}}{6 c^{3}}$$

Divide each polynomial by the binomial. $$\left(p^{2}+11 p+16\right) \div(p+8)$$

Mixed Practice $$\frac{27 a^{7}}{3 a^{3}}+\frac{54 a^{9}}{9 a^{5}}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.