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
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