Add or subtract, as indicated. See Example 2. 3(8p^2-5p) - 5(3p^2-2p+4)

Verified step by step guidance

1. Distribute the 3 into the first expression: \(3(8p^2 - 5p) = 3 \times 8p^2 - 3 \times 5p\).
2. Simplify the first expression: \(24p^2 - 15p\).
3. Distribute the -5 into the second expression: \(-5(3p^2 - 2p + 4) = -5 \times 3p^2 + 5 \times 2p - 5 \times 4\).
4. Simplify the second expression: \(-15p^2 + 10p - 20\).
5. Combine like terms from both expressions: \((24p^2 - 15p) - (15p^2 - 10p - 20)\).

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. In the given expression, applying the distributive property is essential to simplify the terms correctly before combining 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 and is crucial for obtaining a final answer. In the expression provided, after distributing, you will need to identify and combine the coefficients of similar terms.

Polynomial Operations

Polynomial operations include addition, subtraction, and multiplication of polynomials. Understanding how to perform these operations is vital for manipulating algebraic expressions. The question requires both distribution and subtraction of polynomials, which are foundational skills in algebra.