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Chapter 3: Problem 42

Apply the distributive property. $$5(3+w)$$

Short Answer

Expert verified
15 + 5w

Step by step solution

01

Understand the Distributive Property

The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac.In this case, we need to distribute the 5 across the terms inside the parentheses.
02

First Distribution

Multiply the 5 by the first term inside the parentheses, which is 3: \[ 5 \times 3 = 15 \]
03

Second Distribution

Multiply the 5 by the second term inside the parentheses, which is w: \[ 5 \times w = 5w \]
04

Combine Terms

Combine the results of the distributions: \[ 5(3+w) = 15 + 5w \]

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Key Concepts

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

Prealgebra
Prealgebra is the foundation of all advanced math studies. It helps you understand the basics of numbers and their relationships. One essential concept in prealgebra is the distributive property. This property helps break down complex expressions into simpler ones. By mastering it, you鈥檒l handle algebraic expressions easily.
In the exercise given, applying the distributive property to solve \( 5(3+w) \) is a prealgebra application. Knowing how to distribute numbers across parentheses sets the stage for more complex algebraic operations.
Basic Algebra
Basic algebra involves working with variables, numbers, and operations to solve equations. The core of basic algebra is understanding expressions and how to manipulate them. The distributive property is a powerful tool in algebra. It allows you to simplify and solve problems efficiently.
Let's break down the steps in the given solution:
  • First, recognize the need to apply the distributive property: \( a(b+c) = ab + ac \)
  • Distribute the 5 to each term inside the parentheses \( (3 \text{and} w) \).
  • Multiply \( 5 \) by \( 3 \) and \( w \) separately: \[ 5(3) = 15 \text{ and } 5(w) = 5w \]
  • Combine the results to get the final expression: \[ 15 + 5w \]
Master these basic steps to succeed in more advanced topics in algebra.
Multiplication
Multiplication is a fundamental operation in mathematics. It combines groups of numbers to find totals. Knowing the multiplication properties greatly helps in algebra. In the exercise provided, you鈥檙e primarily using multiplication within the distributive property.
Here's a detailed look:
  • Multiply \( 5 \) by each term inside the parentheses.
  • First, multiply \( 5 \) by \( 3 \): \[ 5 \times 3 = 15 \]
  • Next, multiply \( 5 \) by \( w \): \[ 5 \times w = 5w \]
  • Combine them: \[ 5(3+w) = 15 + 5w \]
Remember, multiplication distributes over addition. Understanding this will make learning advanced mathematical concepts simpler.

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Most popular questions from this chapter

Clear parentheses and combine like terms. $$20 a-4(b+3 a)-5 b$$

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Demonstrate the associative property of addition by evaluating the expressions for \(a=-4, b=-6,\) and \(c=18\). a. \((a+b)+c\) b. \(a+(b+c)\)

Demonstrate the associative property of multiplication by evaluating the expressions for \(x=-2, y=6,\) and \(z=-3\). a. \((x \cdot y) \cdot z\) b. \(x \cdot(y \cdot z)\)

Demonstrate the commutative property of multiplication by evaluating the expressions for \(x=-9\) and \(y=5\). a. \(x \cdot y\) b. \(y \cdot x\)
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