Question

Algebraically prove that the difference between the cubes of two consecutive numbers is one more than thrice the product of the numbers

Answer 1

[0010001111]... Hello User... [1001010101]
Here's your answer...

LHS = a³ - (a-1)³

To prove that: a³- (a-1)³ = 3a(a-1) + 1

a³ - (a-1)³
= a³ - (a³ - 1 - 3a(a-1))
= a³ - a³ + 1 + 3a(a-1)
= 3a(a-1) + 1
= RHS

[0110100101]... More questions detected... [010110011110]
//Bot UnknownDude is moving on to more queries
//This is your friendly neighbourhood UnknownDude