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Difference of Cubes Formula

The Difference of Cubes Formula states that –

\[\LARGE a^{3}-b^{3}=(a+b)(a^{2}+ab+b^{2})\]

Solved Examples

Question 1: What is a 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 $\times$ (25 + 15 + 9)
= 7 $\times$ 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 $\times$ (196 + 98 + 49)
= 7 $\times$ 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