/*! 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 72 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 72

Use the distributive property to expand \(4 x(5 y+11)\).

Short Answer

Expert verified
Question: Expand the expression \(4x(5y+11)\) using the distributive property. Answer: \(20xy + 44x\)

Step by step solution

01

Apply the distributive property

We need to multiply \(4x\) by both terms inside the parentheses. So, we have: \(4x(5y+11) = 4x \cdot 5y + 4x \cdot 11\)
02

Multiply the terms

Now, we will multiply the terms as follows: \(4x \cdot 5y + 4x \cdot 11 = 20xy + 44x\)
03

Write the final result

The expanded expression using the distributive property is: \(4x(5y+11) = 20xy + 44x\)

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 Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and mathematical operators like addition and multiplication. In our exercise, the expression \(4x(5y+11)\) involves variables \(x\) and \(y\), numbers 4, 5, and 11, and operations of multiplication and addition. These expressions are essential because they allow us to represent relationships and changes mathematically.
  • Numbers: Constants that do not change (e.g., 4, 5, 11).
  • Variables: Symbols that represent unknown numbers (e.g., \(x, y\)).
  • Terms: Parts of the expression separated by addition or subtraction (e.g., \(4x \, ext{and} \, 5y\)).
Understanding algebraic expressions is crucial as it forms the foundation for solving equations and performing various algebraic operations.
Multiplication
Multiplication is one of the basic arithmetic operations used to find the product of two numbers or expressions. It is a shortcut for repeated addition. In algebra, multiplication is often used to simplify and expand expressions.In our problem, \(4x\) is multiplied by each term within the parentheses \((5y + 11)\). This means:
  • Multiply \(4x\) by \(5y\), resulting in \(20xy\).
  • Multiply \(4x\) by 11, resulting in \(44x\).
Multiplication should be performed with care, especially when dealing with variables, as it requires combining both coefficients and variables correctly.
Expansion
Expansion in algebra refers to the process of removing parentheses by multiplying the terms inside the parentheses with those outside. This process, also known as using the distributive property, allows us to express an algebraic expression in a different form.To expand \(4x(5y+11)\) using the distributive property, we follow these steps:
  • Distribute \(4x\) to both \(5y\) and 11.
  • Compute \(4x \cdot 5y = 20xy\).
  • Compute \(4x \cdot 11 = 44x\).
Through expansion, complex algebraic expressions become simpler to work with, enabling further manipulation and simplification.
Polynomials
Polynomials are a type of algebraic expression that incorporates variables raised to whole number exponents and their coefficients. They are typically summed up terms like \(ax^n + bx^{n-1} + \ldots + c\). Understanding polynomials is important for many areas within mathematics and applied sciences.The expanded expression from the exercise, \(20xy + 44x\), is an example of a polynomial:
  • Polynomial Terms: \(20xy\) and \(44x\)
  • Variables: \(x, y\)
  • Coefficients: 20 for \(xy\) term and 44 for \(x\) term
By learning how to handle polynomials, we gain the ability to solve complex mathematical problems involving equations, functions, and more.

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

For the following problems, convert the numbers from scientific notation to standard decimal form. Light travels about \(5.866 \times 10^{12}\) miles in one year.

Convert the numbers used in the following problems to scientific notation. In 1981 , a Japanese company built the largest oil tanker to date. The ship has a mass of about 510,000,000,000 grams. This oil tanker is more than 6 times as massive as the U.S. aircraft carrier, U.S.S. Nimitz.

For the following problems, convert the numbers from scientific notation to standard decimal form. A mitochondrion is the energy-producing element of a cell. A mitochondrion is about \(1.5 \times 10^{-6}\) meters in diameter.

Perform each multiplication. $$ \left(5 \times 10^{18}\right)\left(3 \times 10^{6}\right) $$

Find the value of each of the following expressions. $$ -5[(-1+5)+(6-8)] $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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.