Question

Without actually calculating the cubes finding the value of 48 cube minus 30 cube minus 18 cube

Answer 1

Answer:

77760

Step-by-step explanation:

48 - 30 -18 = 0

Therefore,

a³+b³+c³= 3abc when a+b+c = 0

Substituting the values,

3 x 48 x -30 x -18 = 77760

Answer 2

Step-by-step explanation:

Method 1

a+b+c = 0 as 48+(-30)+(-18) = 0

So, a^3 + b^3 ^ + c ^3 = 3abc

3abc = 3*48*30*18 = 77760

Method 2 (Normal calculation)

48^3= (50-2)^2 x (50-2)

= (2500+4-200)(50-2)

= (2304)(50-2)

= (115200-4608) = 110592

18^3 = (20-2)^3

= (20-2)^2 x (20-2)

= (400+4-80)(20-2)

= (484)(20-2)

= (9680-968)

= 8712

So,

48 cube minus 30 cube minus 18 cube = 110592 - 27000 - 8712 = 77760