Rewrite each expression using the distributive property and simplify, if possible. See Example 7.7r - 9r

Verified step by step guidance

1. Identify the common factor in the expression: both terms have 'r' as a common factor.
2. Apply the distributive property: factor out the common factor 'r' from each term.
3. Rewrite the expression as: r(7 - 9).
4. Simplify the expression inside the parentheses: calculate 7 - 9.
5. The expression simplifies to: r(-2).

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside parentheses, effectively distributing the multiplication across the terms. It is essential for simplifying expressions and solving equations in algebra.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions by consolidating similar terms into a single term, making calculations easier and clearer. For example, in the expression 7r - 9r, both terms are like terms and can be combined.

Simplification of Expressions

Simplification of expressions refers to the process of reducing an expression to its simplest form. This can involve combining like terms, applying the distributive property, and eliminating any unnecessary components. The goal is to make the expression easier to work with, which is crucial for solving equations or performing further calculations.