Without actually calculating the cubes, find the value of 48³ - 30³ - 18³

Solution:

Given, 48³ - 30³ - 18³

We have to find the value of 48³ - 30³ - 18³ without actually calculating the cubes.

We know that x³ + y³ + z³ - 3xyz = (x + y + z) (x² + y² + z² - xy - yz - zx)

If x + y + z = 0, then x³ + y³ + z³ - 3xyz = 0 (or) x³ + y³ + z³ = 3xyz.

Here, x = 48; y = -30; z = -18

x + y + z = 48 - 30 - 18

= 48 - 48

= 0

x + y + z = 0

So, x³ + y³ + z³ = 3xyz.

48³ - 30³ - 18³ = 3(48)(-30)(-18)

= 144(540)

= 77760

Therefore, 48³ - 30³ - 18³ = 77760

✦ Try This: Without actually calculating the cubes, find the value of 47³ - 31³ - 16³

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Sample Problem 3(i)

Without actually calculating the cubes, find the value of 48³ - 30³ - 18³.

Summary:

Without actually calculating the cubes, the value of 48³ - 30³ - 18³ is 77760

☛ Related Questions:

• Without finding the cubes, factorise (x - y)³ + (y - z)³ + (z - x)³
• x² + x + 1. Classify the following polynomial as polynomials in one variable, two variables etc
• y³ - 5y. Classify the following polynomial as polynomials in one variable, two variables etc