Problem 29 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$8(2 x+3)$$

Step-by-Step Solution

Answer

The answer is \(16x + 24\).

Step 1: Distributive Property

The distributive property in algebra tells us that for any numbers a, b, and c, the expression a(b + c) is equal to ab + ac. In simple terms, the distributive property of multiplication over addition allows us to get rid of the parentheses by multiplying each term inside the parentheses by the factor outside of them.

Step 2: Apply the Distributive Property

In the given problem, you have 8 being multiplied by the contents of the parentheses: \(2x + 3\). Applying the distributive property means multiplying 8 with each term inside the parentheses. Multiply 8 with \(2x\) to get \(16x\), and multiply 8 with 3 to get 24.

Step 3: Write out the Result

Combine the terms from the previous step to form the final expression. In this case, combining \(16x\) and 24 to get the final expression of \(16x + 24\).