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 distributive property formula: \(a(b + c) = ab + ac\). This means you multiply the term outside the parentheses by each term inside the parentheses.
2. Apply the distributive property to the expression \$2(m + p)$ by multiplying 2 with each term inside the parentheses separately.
3. Write the multiplication as \(2 \times m + 2 \times p\).
4. Simplify the expression by writing it as \$2m + 2p$.
5. Check if the expression can be simplified further by combining like terms; since \$2m\( and \)2p\( are unlike terms, the expression \)2m + 2p$ is already simplified.

Key Concepts

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually by the number and then adding the products. For example, a(b + c) = ab + ac. This property is essential for expanding expressions like 2(m + p).

Simplification of Algebraic Expressions

Simplification involves combining like terms and reducing expressions to their simplest form. After applying the distributive property, terms such as 2m and 2p can be combined if possible, making the expression easier to work with or interpret.

Understanding Variables and Constants

Variables represent unknown or changing quantities, while constants are fixed numbers. Recognizing which parts of the expression are variables (m, p) and which are constants (2) helps in correctly applying operations like multiplication and simplification.