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 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

⇒ a3 = 513 + 63

⇒ a3 = 729

⇒ a = 9

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Practise This Question

If the dipole moment of CH3F is 1.847 D, the dipole moment of CD3F will be

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