Question

algebraically prove that the difference between the the the cubes of two consecutive numbers is one more than thrice the product of the the numbers .is it true for negative integers also ? justify your answers with examples.

Answer 1

Let the numbers with x and x + 1

Now,

Difference between the cubes of the number

=(x+1)³-x³

=x³+1+3x(x+1)-x³

=3.x.(x+1) +1

=3.product of numbers+1

Hence, proved that the difference between the cubes of two consecutive number is equal to one more than the the thrice the product of the numbers.