Question

Show that if a number is doubled , then it's cube becomes eight times the cube of the given number ??

Answer 1

number=x
cube=x^3
doubled number = 2x
its cube = (2x)^3
= 8x^3
Therefore it is 8 times the cube of the given number

Answer 2

Answer:

To prove: If a number is doubled then its cube is 8 times the cube of the given number.

Proof: Let the number be 'a'

The double of the number = 2a

Cube of the number = a3

According to the given problem, 

Cube of 2a (double of the number) = ( 2a)3 

                                                        = 8 a3 

                                                        = 8 x ( cube of the  number )

                                                        = 8 times the cube of the number

Hence Proved.