Simplify each expression. See Example 8. 3(k + 2) - 5k + 6 + 3

Verified step by step guidance

1. First, rewrite the expression clearly: \$3(k + 2) - 5k + 6 + 3$.
2. Apply the distributive property to \$3(k + 2)$, which means multiply 3 by each term inside the parentheses: \(3 \times k + 3 \times 2\).
3. This gives \$3k + 6\(, so now the expression becomes \)3k + 6 - 5k + 6 + 3$.
4. Next, combine like terms. Group the terms with \(k\): \$3k - 5k\(, and group the constant terms: \)6 + 6 + 3$.
5. Simplify each group: \$3k - 5k\( becomes \)(3 - 5)k\(, and \)6 + 6 + 3$ becomes the sum of those constants.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, in 3(k + 2), multiply 3 by k and 3 by 2 separately, resulting in 3k + 6. This step is essential for simplifying expressions with parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, terms like 3k and -5k can be combined to simplify the expression. This process reduces the expression to its simplest form.

Simplification of Constants

Simplification of constants means adding or subtracting the numerical values without variables. In the expression, constants like 6 and 3 can be combined to get 9. This step helps in reducing the expression to a simpler numerical form.