Problem 41 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$(2 x+7) 4$$

Step-by-Step Solution

Answer

The algebraic expression without parentheses is \(8x + 28\).

Step 1: Applying Distributive Property

Use the distributive property to distribute the number outside the parentheses, which is 4, to each term inside the parentheses. The distributive property states that for all real numbers a, b, and c, a(b + c) = ab + ac. Thus, \(4 \times (2x + 7)\) becomes \(4 \times 2x + 4 \times 7\).

Step 2: Multiplication of Coefficients/Constansts

Next, perform multiplication. \(4 \times 2x = 8x\) and \(4 \times 7 = 28\). So, the expression further simplifies to \(8x + 28\).