Question

(p³-3k)(p²+3k)-(p²-3k)(p³+3k)

Answer 1

Ответ:

(p³-3k)(p²+3k)-(p²-3k)(p³+3k)=р^5+3kp³-3kp²-9k²-(p^5+3kp³-3kp²-9k²)=

=р^5+3kp³-3kp²-9k²-p^5-3kp³+3kp²+9k²=6kp³-6kp²=6kp²(k-1)

Объяснение:

Answer 2

To simplify the expression, let's expand it step by step:

(p³ - 3k)(p² + 3k) - (p² - 3k)(p³ + 3k)

Expanding the first set of parentheses:

= p³ * p² + p³ * 3k - 3k * p² - 3k * 3k

= p^5 + 3kp³ - 3kp² - 9k²

Expanding the second set of parentheses:

= p² * p³ + p² * 3k - 3k * p³ - 3k * 3k

= p^5 + 3kp² - 3kp³ - 9k²

Now subtracting the second expression from the first:

(p^5 + 3kp³ - 3kp² - 9k²) - (p^5 + 3kp² - 3kp³ - 9k²)

This simplifies to:

p^5 + 3kp³ - 3kp² - 9k² - p^5 - 3kp² + 3kp³ + 9k²

The terms p^5 and -p^5 cancel out, as well as the terms 9k² and -9k²:

= 3kp³ - 3kp² + 3kp³ - 3kp²

Combining like terms:

= 6kp³ - 6kp²

So, the simplified expression is 6kp³ - 6kp².