Rewrite each expression using the distributive property and simplify, if possible. See Example 7.-12(x - y)

Verified step by step guidance

1. Identify the expression to be simplified: \(-12(x - y)\).
2. Apply the distributive property: Multiply \(-12\) by each term inside the parentheses.
3. Calculate \(-12 \times x\) to get \(-12x\).
4. Calculate \(-12 \times (-y)\) to get \(+12y\).
5. Combine the results to rewrite the expression as \(-12x + 12y\).

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 within a set of parentheses, effectively distributing the multiplication across the terms. It is essential for simplifying expressions and solving equations in algebra.

Combining Like Terms

Combining like terms involves simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This process helps to reduce the expression to its simplest form, making it easier to understand and work with.

Simplification of Expressions

Simplification of expressions refers to the process of reducing an expression to its most concise form. This can involve applying the distributive property, combining like terms, and performing arithmetic operations. The goal is to make the expression easier to interpret and solve.