Rewrite each expression using the distributive property and simplify, if possible. See Example 7.2 (x - 3y + 2z)

Verified step by step guidance

1. Identify the expression inside the parentheses: \(x - 3y + 2z\).
2. Apply the distributive property: multiply each term inside the parentheses by 2.
3. Calculate \(2 \times x\) to get \(2x\).
4. Calculate \(2 \times (-3y)\) to get \(-6y\).
5. Calculate \(2 \times 2z\) to get \(4z\).

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 and trigonometry.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form by combining like terms and eliminating unnecessary components. In the context of the distributive property, this means after distributing, you should combine any similar terms to make the expression more manageable and easier to interpret.

Like Terms

Like terms are terms that contain the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 4y are not. Identifying and combining like terms is crucial in the simplification process, as it allows for a more concise expression and clearer understanding of the mathematical relationships involved.