Problem 27 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The simplified form of the algebraic expression \(3(x + 5)\) is \(3x + 15\).

Step 1: Identify the common factor

In this exercise, the common factor across all terms in the parentheses is \(3\). This will be distributed to all the terms inside the parentheses.

Step 2: Apply the Distributive Property

Use the distributive property to multiply the \(3\) with each term inside the parentheses, i.e., multiply \(3\) with \(x\) to get \(3x\) and multiply \(3\) with \(5\) to get \(15\).

Step 3: Combine the results

After multiplying, combine the multiplied values \(3x\) and \(15\) together.