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Chapter 1: Problem 45

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$5(3 x-2+4 y)$$

Short Answer

Expert verified
The expression \(5(3x - 2 + 4y)\) without parentheses, using the distributive property, is \(15x - 10 + 20y\).

Step by step solution

01

Identify the terms inside the parentheses

There are three terms inside the parentheses: \(3x\), \(-2\), and \(4y\).
02

Apply the distributive property

Multiply the term outside the parentheses (5) by each of the terms inside the parentheses. This gives: \(5 \cdot 3x\), \(5 \cdot -2\), and \(5 \cdot 4y \)
03

Perform the multiplication

Perform the multiplication for all the terms obtained in step 2. The new expression becomes: \(15x -10 + 20y \)

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Most popular questions from this chapter

The list shows a pattern for various products. $$\begin{aligned}2(-3) &=-6 \\\1(-3) &=-3 \\\0(-3) &=0 \\\\-1(-3) &=3 \\\\-2(-3) &=6 \\\\-3(-3) &=9 \\\\-4(-3) &=? \end{aligned}$$ Use this pattern to find \(-4(-3)\)

Perform the indicated subtraction. $$\frac{2}{5}-\frac{1}{10}$$

Simplify each series of additions and subtractions. $$13-2-(-8)$$

Explain how to subtract real numbers.

Perform the indicated subtraction. $$\frac{1}{2}-\frac{1}{4}$$
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