Answer:
To simplify the expression, you can start by factoring common terms:
P²n(2p³ - 5p + 6) - pn(p⁴ - 3p² + 4p) - 2n(p³ - p² - 3)
First, let's factor common terms out of each part of the expression:
1. Factor P²n out of the first part:
P²n(2p³ - 5p + 6) = P²n(2p³) - P²n(5p) + P²n(6) = 2p⁵n - 5p³n + 6p²n
2. Factor pn out of the second part:
pn(p⁴ - 3p² + 4p) = pn(p⁴) - pn(3p²) + pn(4p) = p⁵n - 3p³n + 4p²n
3. Factor 2n out of the third part:
2n(p³ - p² - 3) = 2n(p³) - 2n(p²) - 2n(3) = 2p³n - 2p²n - 6n
Now, you can combine all the simplified parts:
(2p⁵n - 5p³n + 6p²n) - (p⁵n - 3p³n + 4p²n) - (2p³n - 2p²n - 6n)
Next, simplify further:
2p⁵n - 5p³n + 6p²n - p⁵n + 3p³n - 4p²n - 2p³n + 2p²n + 6n
Now, combine like terms:
(2p⁵n - p⁵n) + (-5p³n + 3p³n - 2p³n) + (6p²n - 4p²n + 2p²n) + 6n
Simplify:
p⁵n - 4p³n + 4p²n + 6n
So, the simplified expression is p⁵n - 4p³n + 4p²n + 6n.
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Answers & Comments
Answer:
To simplify the expression, you can start by factoring common terms:
P²n(2p³ - 5p + 6) - pn(p⁴ - 3p² + 4p) - 2n(p³ - p² - 3)
First, let's factor common terms out of each part of the expression:
1. Factor P²n out of the first part:
P²n(2p³ - 5p + 6) = P²n(2p³) - P²n(5p) + P²n(6) = 2p⁵n - 5p³n + 6p²n
2. Factor pn out of the second part:
pn(p⁴ - 3p² + 4p) = pn(p⁴) - pn(3p²) + pn(4p) = p⁵n - 3p³n + 4p²n
3. Factor 2n out of the third part:
2n(p³ - p² - 3) = 2n(p³) - 2n(p²) - 2n(3) = 2p³n - 2p²n - 6n
Now, you can combine all the simplified parts:
(2p⁵n - 5p³n + 6p²n) - (p⁵n - 3p³n + 4p²n) - (2p³n - 2p²n - 6n)
Next, simplify further:
2p⁵n - 5p³n + 6p²n - p⁵n + 3p³n - 4p²n - 2p³n + 2p²n + 6n
Now, combine like terms:
(2p⁵n - p⁵n) + (-5p³n + 3p³n - 2p³n) + (6p²n - 4p²n + 2p²n) + 6n
Simplify:
p⁵n - 4p³n + 4p²n + 6n
So, the simplified expression is p⁵n - 4p³n + 4p²n + 6n.