Question

Simplify the expression -3p³ + 5p(-2p²)(-4) - 12p⁵ - (-8p³), and select the answer in descending powers of p.

A) -5p³ + 2p² - 7p - 1
B) 5p³ - 2p² + 7p - 1
C) 1 - 7p - 2p² + 5p³
D) 2p² - 5p³ - 1 + 7p

Answer 1

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.