Simplify each expression. See Example 8.0.25(8 + 4p) - 0.5(6 + 2p)

Verified step by step guidance

1. Distribute the 0.25 into the expression (8 + 4p) to get 0.25 * 8 + 0.25 * 4p.
2. Calculate 0.25 * 8 to simplify the first term.
3. Calculate 0.25 * 4p to simplify the second term.
4. Distribute the -0.5 into the expression (6 + 2p) to get -0.5 * 6 - 0.5 * 2p.
5. Combine like terms from the results of the distributions to simplify the expression further.

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 inside a parenthesis, which is essential for simplifying expressions. In the given expression, applying the distributive property will help eliminate the parentheses and combine like terms effectively.

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, making it easier to work with. In the expression provided, after applying the distributive property, you will need to combine the constant terms and the terms involving 'p' to reach a simplified form.

Simplification of Expressions

Simplification of expressions is the process of reducing an expression to its simplest form, which often involves performing operations like addition, subtraction, multiplication, and division. This is crucial in algebra and trigonometry as it allows for clearer understanding and easier manipulation of equations. The goal is to express the original expression in a more concise and manageable way.