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Question
Simplify:
p3 − (p + 1)3
Solution 1
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
p3 − (p + 1)3
= {p − (p + 1)} {(p)2 + (p + 1)2 + (p) × (p + 1)}
= (−1) (p2 + p2 + 1 + 2p + p2 + p)
= (−1)(3p2 + 3p + 1)
= −3p2 − 3p − 1
Solution 2
p3 − (p + 1)3
We know that,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= p3 − (p3 + 3p2 + 3p + 1)
= p3 − p3 − 3p2 − 3p − 1
= −3p2 − 3p − 1
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