Final answer:
To simplify the expression, combine like terms and arrange them in descending powers of p.
Step-by-step explanation:
To simplify the expression -3p³ + 5p(-2p²)(-4) - 12p⁵ - (-8p³), we need to perform the operations in the correct order following the rules of algebra.
First, we simplify the terms inside the parentheses: -2p² multiplied by -4 gives us 8p².
Next, we combine like terms. The terms involving p³ are -3p³ and -8p³, which add up to -11p³. The term involving p² is 5p(8p²), which gives us 40p³. The term involving p⁵ is -12p⁵.
Combining all these terms, we have -11p³ + 40p³ - 12p⁵. Rearranging the terms in descending powers of p, we get -12p⁵ + 29p³.