Simplify each expression. See Example 8.10 - (4y + 8)

Verified step by step guidance

1. Start by distributing the negative sign across the terms inside the parentheses: \( -(4y + 8) \) becomes \(-4y - 8\).
2. Rewrite the expression by replacing the original parentheses with the distributed terms: \(10 - 4y - 8\).
3. Combine like terms by subtracting 8 from 10: \(10 - 8\).
4. Simplify the expression: \(2 - 4y\).
5. The simplified expression is \(2 - 4y\).

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, facilitating the simplification of expressions. In the given expression, applying the distributive property helps to eliminate the parentheses and combine like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions by consolidating similar components into a single term, making it easier to work with. In the expression provided, after applying the distributive property, combining like terms will lead to a more simplified result.

Simplification of Expressions

Simplification of expressions is the process of reducing an expression to its simplest form, which often involves removing parentheses, combining like terms, and performing arithmetic operations. The goal is to make the expression easier to understand and work with. In this case, simplifying the expression will yield a clearer and more concise result.