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 by each term inside the parentheses separately.
3. Multiply 2 by \(m\) to get \(2 \times m = 2m\).
4. Multiply 2 by \(p\) to get \(2 \times p = 2p\).
5. Write the simplified expression by combining the two products: \$2m + 2p$.

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 allows us to simplify expressions by removing parentheses.

Simplifying Algebraic Expressions

Simplifying involves combining like terms and performing arithmetic operations to write an expression in its simplest form. After applying the distributive property, terms with the same variables and exponents can be combined to reduce the expression.

Multiplication of Variables and Constants

When multiplying a constant by a variable or sum of variables, the constant multiplies each term inside the parentheses. Understanding how to multiply constants with variables correctly is essential to apply the distributive property and simplify expressions.