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

Verified step by step guidance

1. First, apply the distributive property to each term inside the parentheses. Multiply 3 by each term in the first parentheses: \$3 \times 8p^2\( and \)3 \times (-5p)$.
2. Next, apply the distributive property to the second parentheses, multiplying -5 by each term inside: \(-5 \times 3p^2\), \(-5 \times (-2p)\), and \(-5 \times 4\).
3. Rewrite the expression with the distributed terms: \$24p^2 - 15p - 15p^2 + 10p - 20$.
4. Combine like terms by grouping the \(p^2\) terms together and the \(p\) terms together: \((24p^2 - 15p^2) + (-15p + 10p) - 20\).
5. Simplify each group to get the final expression in standard form, combining coefficients of like terms.

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 expanding expressions like 3(8p^2 - 5p) by multiplying 3 with each term inside the parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, 8p^2 and -15p^2 can be combined because both are terms with p squared. This simplifies the expression after distribution.

Polynomial Subtraction

Polynomial subtraction requires careful attention to signs when subtracting one polynomial from another. You must distribute the negative sign across all terms in the second polynomial before combining like terms to avoid errors.