Problem 34 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The expression \(7(x+y)\) can be rewritten without parentheses as \(7x + 7y\) by using the distributive property of multiplication over addition.

Step 1: Identify the terms

The given algebraic expression is \(7(x+y)\). Here, 7 is the numerical coefficient, while x and y are the variables inside the brackets.

Step 2: Apply the distributive property

Applying the distributive property, multiply the outside term (7 in this case) by each of the terms inside the parentheses (x and y). Hence, \(7(x+y)\) becomes \(7*x + 7*y\).

Step 3: Simplify the new expression

The resulting expression after applying the distributive property is \(7*x + 7*y\), or in standard form \(7x + 7y\) without any parentheses.