 # Difference of Cubes Formula

The difference of cubes formula in algebra is used to calculate the value of the algebraic expression (a3 – b3). In simple words, it is used to equate the difference of two cube values.

## Formula for Difference of Cubes in Algebra

The formula to find the difference of two cubes is given as:

 a3 – b3 = (a – b) (a2 + ab + b2)

Also Check: Sum of Cubes Formula

### Solved Examples Using the Difference of Cubes Formula

Question 1: What is the value of 53 – 33?

Solution:

The difference of cubes formula is, a3 – b3 = (a – b)(a2 + ab + b2)

From the given expression, a = 5 ; b = 3

53 – 33 = (5 – 3) (52 + (5)(3) + 32)

= 2 × (25 + 15 + 9)

= 2 × 49

= 98

Question 2: What is the value of 143 – 73?

Solution:

The difference of cubes formula is,

a3 – b3 = (a – b) (a2 + ab + b2)

From the given expression,

a = 14 ; b = 7

⇒ 143 – 73 = (14 – 7) (142 + (14)(7) + 72)

= 7 × (196 + 98 + 49)

= 7 × 343

= 2401

Question 3: Find the value of a, if a3 – 63 = 513

Solution:

As per the formula, a3 – b3 = (a – b) (a2 + ab + b2)

a3 – 63 = 513

⇒ a3 = 513 + 63

⇒ a3 = 513 + 216

⇒ a3 = 729

⇒ a = 9