Rewrite each expression using the distributive property and simplify, if possible. See Example 7.2(m + p)

Verified step by step guidance

1. Identify the expression to be simplified: \(2(m + p)\).
2. Apply the distributive property: Multiply 2 by each term inside the parentheses.
3. Calculate \(2 \times m\) to get \(2m\).
4. Calculate \(2 \times p\) to get \(2p\).
5. Combine the results to rewrite the expression as \(2m + 2p\).

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a set of parentheses, effectively distributing the multiplication across the terms. It is a fundamental principle in algebra that simplifies expressions and is essential for solving equations.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form by combining like terms and eliminating unnecessary components. In the context of the distributive property, this means performing the multiplication and then combining any similar terms that may arise, making the expression easier to work with.

Like Terms

Like terms are terms that contain the same variable raised to the same power. For example, 2m and 3m are like terms because they both contain the variable m. Identifying and combining like terms is crucial during simplification, as it allows for a more concise expression and clearer understanding of the mathematical relationships involved.