/*! 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 357 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 357

In the following exercises, simplify using the Distributive Property. $$ (y+4) p $$

Short Answer

Expert verified
py + 4p

Step by step solution

01

Understand the Distributive Property

The Distributive Property states that for any numbers or expressions a, b, and c: \[a(b + c) = ab + ac\]In this case, we have \[(y + 4)p\].So, we will use the Distributive Property to distribute 'p' across the sum inside the parentheses.
02

Distribute 'p' to each term inside the parentheses

Distribute 'p' to both 'y' and '4'. This results in:\[p \times y + p \times 4\]
03

Simplify the expression

Multiply 'p' with 'y' and 'p' with '4':\[p \times y = py\]\[p \times 4 = 4p\]Combine these results to get:\[py + 4p\]

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 combinations of variables, numbers, and operations. In our exercise, the expression is \[(y+4)p\]. Here, 'y' is a variable, '4' is a constant, and 'p' is another variable. When working with algebraic expressions, we often need to perform operations like addition, subtraction, multiplication, and division. For example, the given expression involves multiplication and addition. It is important to remember that variables represent unknown values, while constants are fixed numbers. Breaking down and understanding each part of the expression is crucial for simplifying and solving algebraic problems.
Simplification
Simplification in algebra involves reducing an expression to its simplest form. The goal is to make the expression easier to work with and understand. In the case of \[(y+4)p\], simplification involves using the Distributive Property to eliminate the parentheses. To do this, we distribute 'p' to both 'y' and '4'.
  • We multiply 'p' by 'y' to get 'py'.
  • We multiply 'p' by '4' to get '4p'.
Combining these terms gives us the simplified expression \py + 4p\. Always ensure each step in simplification is clear and logical to avoid making errors.
Intermediate Algebra
Intermediate algebra builds on basic algebra concepts, introducing more complex operations and properties. The Distributive Property is a fundamental principle often used in intermediate algebra. It allows us to simplify expressions and solve equations more efficiently. For example, understanding that \a(b + c) = ab + ac\ helps us break down and simplify \[(y + 4)p\] into \py + 4p\. This knowledge is foundational for solving more advanced problems involving multiple variables, linear equations, and polynomials. Practicing these techniques solidifies our ability to manipulate and simplify algebraic expressions across a variety of contexts.

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

When the Szetos sold their home, the selling price was \(500 \%\) of what they had paid for the house 30 years ago. Explain what \(500 \%\) means in this context.

In the following exercises, simplify using the Distributive Property. $$ (4 y-1)-(y-2) $$

In the following exercises, write each decimal as a fraction. $$ 1.464 $$

In the following exercises, simplify. $$ 0 \div\left(y-\frac{1}{6}\right), \text { where } x \neq \frac{1}{6} $$

In the following exercises, simplify using the Distributive Property. $$ 18-4(x+2) $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.