Question

Simplify:

p³ − (p + 1)³

Answer 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

Answer 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