Simplify each expression. See Example 8. 10 - (4y + 8)

Verified step by step guidance

1. Identify the expression to simplify: \$10 - (4y + 8)$.
2. Apply the distributive property to remove the parentheses by multiplying the minus sign with each term inside the parentheses: \$10 - 4y - 8$.
3. Combine like terms by subtracting the constants: \$10 - 8$.
4. Rewrite the expression with the combined constants and the variable term: \((10 - 8) - 4y\).
5. Simplify the constants to get the final simplified expression: \$2 - 4y$.

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 simplifying expressions like 10 - (4y + 8) by distributing the negative sign across the terms inside the parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions by reducing the number of terms. For instance, after distributing, terms like -4y and any other y-terms can be combined to simplify the expression.

Simplifying Algebraic Expressions

Simplifying algebraic expressions means rewriting them in a simpler or more compact form without changing their value. This includes removing parentheses, combining like terms, and performing arithmetic operations. It helps in making expressions easier to understand and work with.