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Chapter 1: Problem 46

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$4(5 x-3+7 y)$$

Short Answer

Expert verified
The algebraic expression \(4(5x - 3 + 7y)\) rewritten without parentheses using the distributive property becomes \(20x - 12 + 28y\).

Step by step solution

01

Identify the terms

First, identify the terms of the algebraic expression. In the expression \(4(5x - 3 + 7y)\), the terms inside the parenthesis are \(5x\), \(-3\), and \(7y\). The number 4 is outside the parenthesis.
02

Distribute the term outside the parentheses

Second, distribute the term outside the parentheses (4 in this case) to each term inside the parentheses. This means you will multiply 4 with each term inside. So, \(4 * 5x = 20x\), \(4 * -3 = -12\), and \(4 * 7y = 28y\).
03

Rewrite the expression

Lastly, rewrite the expression without parentheses using the results from step 2. The expression becomes \(20x - 12 + 28y\).

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Most popular questions from this chapter

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 9 times a number and \(-4\) times the number.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(7-(-2)=5\)

Perform the indicated subtraction. $$15-(-15)$$3

Perform the indicated subtraction. $$\frac{1}{7}-\left(-\frac{3}{7}\right)$$

Perform the indicated subtraction. $$\frac{3}{7}-\frac{5}{7}$$
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