Rewrite each expression using the distributive property and simplify, if possible. See Example 7.-(2d - f)

Verified step by step guidance

1. Identify the expression inside the parentheses: \(2d - f\).
2. Apply the distributive property by multiplying each term inside the parentheses by \(-1\).
3. Multiply \(-1\) by \(2d\) to get \(-2d\).
4. Multiply \(-1\) by \(-f\) to get \(+f\).
5. Combine the results to rewrite the expression as \(-2d + f\).

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 parenthesis, effectively distributing the multiplication across the terms. It is essential for simplifying expressions and solving equations, especially when dealing with polynomials.

Negative Sign and Its Effect

A negative sign in front of a parenthesis indicates that all terms inside the parenthesis should be multiplied by -1. This means that each term will change its sign when applying the distributive property. Understanding how to handle negative signs is crucial for correctly simplifying expressions.

Simplification of Expressions

Simplification involves combining like terms and reducing expressions to their simplest form. After applying the distributive property, it is often necessary to combine similar terms to achieve a more concise expression. This process is fundamental in algebra and trigonometry for clearer problem-solving.