Problem 65 Simplify each expression. $$-8... [FREE SOLUTION]

Chapter 3: Problem 65

Simplify each expression. $$-8(r-5)$$

Short Answer

Expert verified

The expression simplifies to $-8r + 40$.

Step by step solution

Distribute the Negative Sign

Start by distributing the negative sign across the parenthesis. This means multiplying -8 with each term inside the parenthesis. The expression is $-8(r - 5)$. Apply the distribution: $-8 \times r = -8r$ and $-8 \times (-5) = +40$.

Simplify the Expression

Combine the terms obtained from distribution. The terms after distribution are $-8r + 40$. We write this as the simplified expression.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

The distributive property is a fundamental algebraic concept that helps to simplify expressions. It involves multiplying a single term by each term within a set of parentheses. For the expression \[-8(r - 5)\], we apply the distributive property by multiplying -8 with $r$ and -5 .

Negative times positive ($-8 \times r$) equals $-8r$.
Negative times negative ($-8 \times -5$) equals $+40$, since two negatives make a positive.

Using the distributive property allows us to break down complex expressions into smaller, more manageable parts, which can then be simplified further.