Problem 43 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$6(x+3+2 y)$$

Step-by-Step Solution

Answer

The algebraic expression \(6(x + 3 + 2y)\) can be rewritten without parentheses as \(6x + 18 + 12y\) using the distributive property.

Step 1: Identify individual terms within the parentheses

The individual terms inside the parentheses are \(x\), \(3\), and \(2y\).

Step 2: Apply the Distributive Property

Now, multiply each term inside the parentheses by 6 using the distributive property. This gives the following: \(6 \cdot x + 6 \cdot 3 + 6 \cdot 2y\).

Step 3: Simplify the Expression

Simplify the resulting expression by performing the multiplications: \(6x + 18 + 12y\)