Rewrite each expression using the distributive property and simplify, if possible. See Example 7.5k + 3k

Verified step by step guidance

1. Identify the common factor in the expression: both terms have 'k' as a common factor.
2. Apply the distributive property: factor out the common factor 'k' from each term.
3. Rewrite the expression as k(5 + 3).
4. Simplify the expression inside the parentheses: add the numbers 5 and 3.
5. The expression simplifies to k(8).

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 parenthesis, facilitating the simplification of expressions. In the context of the given question, it helps in rewriting expressions by distributing coefficients across variables.

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 components, making calculations easier. In the example provided, 5k and 3k are like terms that can be combined to yield a single term.

Simplification of Algebraic Expressions

Simplification of algebraic expressions refers to the process of reducing an expression to its simplest form. This often involves using the distributive property, combining like terms, and eliminating unnecessary parentheses. The goal is to express the equation in a more manageable and understandable format, as seen in the task of rewriting 5k + 3k.