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

Verified step by step guidance

1. Distribute the constants 3 and -2 to each term inside the parentheses: apply the distributive property \(a(b + c) = ab + ac\). So, multiply 3 by both \(m\) and \(-4\), and multiply -2 by both \(m\) and \$1\(. This gives \)3m - 12 - 2m - 2$.
2. Combine like terms by grouping the terms with \(m\) together and the constant terms together. This means combining \$3m\( and \)-2m\(, and combining \)-12\( and \)-2$.
3. Simplify the expression by performing the addition or subtraction of the like terms: \$3m - 2m\( and \)-12 - 2$.
4. Write the simplified expression by putting together the results from the previous step, which will be in the form of \(am + b\), where \(a\) and \(b\) are constants.
5. Review the simplified expression to ensure no further simplification is possible, such as factoring or combining terms.

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, terms with 'm' and constant terms should be grouped and simplified to reduce the expression to its simplest form.

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 constants, which helps in making expressions easier to understand and use.