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 \$5k + 3k\(. Here, both terms have the variable \)k$.
2. Use the distributive property, which states that \(a b + a c = a (b + c)\), to factor out the common variable \(k\) from both terms.
3. Rewrite the expression as \(k (5 + 3)\) by factoring out \(k\).
4. Simplify the expression inside the parentheses by adding the numbers: \$5 + 3$.
5. Write the simplified expression as \(k \times 8\) or simply \$8k$.

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 results. In algebraic terms, a(b + c) = ab + ac. This property helps simplify expressions by factoring or expanding terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 5k and 3k are like terms because both contain the variable k. Adding their coefficients simplifies the expression to 8k.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing operations such as addition, subtraction, multiplication, or division. Simplifying 5k + 3k involves using the distributive property and combining like terms to get a more concise expression.