Simplify each expression. See Example 8.3(m - 4) - 2(m + 1)

Verified step by step guidance

1. Distribute the 3 into the terms inside the first parentheses: \(3(m - 4) = 3m - 12\).
2. Distribute the -2 into the terms inside the second parentheses: \(-2(m + 1) = -2m - 2\).
3. Combine the expressions from the two distributions: \(3m - 12 - 2m - 2\).
4. Combine like terms: \(3m - 2m\) and \(-12 - 2\).
5. Simplify the expression to get the final result.

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 inside a set of parentheses. In the given expression, applying the distributive property is essential to simplify the terms involving 'm' and the constants separately.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplification as it helps to consolidate the expression into a more manageable form. In the expression provided, after distributing, we will combine the coefficients of 'm' and the constant terms.

Simplification of Expressions

Simplification of expressions refers to the process of reducing an expression to its simplest form. This involves performing operations such as addition, subtraction, and factoring where applicable. In the context of the given expression, simplification will lead to a clearer and more concise representation of the mathematical relationship.