Simplify each expression. See Example 8. 3(m - 4) - 2(m + 1)

Verified step by step guidance

1. Identify the expression to simplify: \$3(m - 4) - 2(m + 1)$.
2. Apply the distributive property to both terms: multiply 3 by each term inside the first parentheses and -2 by each term inside the second parentheses, resulting in \(3 \times m - 3 \times 4 - 2 \times m - 2 \times 1\).
3. Rewrite the expression with the distributed terms: \$3m - 12 - 2m - 2$.
4. Combine like terms by grouping the \(m\) terms together and the constant terms together: \((3m - 2m) + (-12 - 2)\).
5. Simplify each group: \$3m - 2m\( simplifies to \)m\(, and \)-12 - 2\( simplifies to \)-14\(, so the simplified expression is \)m - 14$.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This is essential for expanding expressions like 3(m - 4) and -2(m + 1) before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. After distributing, you group terms with 'm' together and constants together to simplify the expression.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing all possible operations. This includes distributing, combining like terms, and reducing the expression to a concise form for easier interpretation or further use.