1.

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

Answer»

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. 

We have to find the value of 

483 – 303 – 183

= 483 + (–30)3 + (–18)3 . 

Here, 48 + (–30) + (–18) = 0 

So, 483 + (–30)3 + (–18)3 

= 3 × 48 × (–30) × (–18)

= 77760


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