Question

The value of 88³ + 12³ – 100³ is equal to ______.

Options

• 3abc

• 2abc

• abc

• 0

Answer 1

The value of 88³ + 12³ – 100³ is equal to 3abc.

Explanation:

When the sum of three numbers a, b and c is zero, the algebraic identity states that the sum of their cubes is three times their product:

a³ + b³ + c³ = 3abc 

This follows from the factorisation: 

a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

Since a + b + c = 0, this factorisation implies: 

a³ + b³ + c³ = 3abc

Hence, the expression a³ + b³ + c³ is equal to 3abc.