Problem 46 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \(4 * 7y = 28y\).

Step 3: Rewrite the expression

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