Difference of Cubes Formula

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

a3 – b3 = (a + b) (a2 + ab + b2)

Solved Examples Using the Formula for Difference of Cubes

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 equation, a = 5 ; b = 3 53 – 33 = (5 – 3) (52 + (5)(3) + 32)
= 2 × (25 + 15 + 9)
= 7 × 49 = 343
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 equation,
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
⇒ a= 513 + 63
⇒ a3 = 729
⇒ a = 9

Practise This Question

NaOH is a strong base because: