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Difference of Cubes Formula

Difference of Cubes Formula is an algebraic formula used to calculate the difference between the cubes of two values. The Difference of Cubes Formula is given as,

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Difference of Cubes Problems

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Some solved problems on difference of cubes are given below:

Solved Examples

Question 1: What is a value of 123 - 53 ?
Solution:
 
The difference of cubes formula is,
a3 - b3 = (a - b)(a2 + ab + b2)
From the given equation,
a = 12 ; b = 5
123 - 53
= (12 - 5) (122 + (12)(5) + 52)
= 7 $\times$ (144 + 60 + 25)
= 7 $\times$ 229
= 1603

 

Question 2: What is the value of 243 - 123 ?
Solution:
 
The difference of cubes formula is,
a3 - b3 = (a - b) (a2 + ab + b2)
From the given equation,
a = 24 ; b = 12
243 - 123
= (24 - 12) (242 + (24)(12) + 122)
= 12 $\times$ (576 + 288 + 144)
= 12 $\times$ 1008
= 12096
 

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