The formula for the difference of two cubes, a^3 – b^3, is a special case of the binomial expansion formula. It can be factored into (a – b)(a^2 + ab + b^2).

Let’s break down the formula and understand its components:

1. (a – b): This part represents the difference between the two values, where ‘a’ and ‘b’ are the values being subtracted. It represents the linear term in the expansion.
2. (a^2 + ab + b^2): This part represents the sum of the squares and the cross product of ‘a’ and ‘b’. It represents the quadratic term in the expansion.

To better understand the formula, let’s expand it using multiplication:

a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Expanding further:

a^3 – b^3 = a(a^2 + ab + b^2) – b(a^2 + ab + b^2)

Using the distributive property of multiplication:

a^3 – b^3 = a^3 + a^2b + ab^2 – a^2b – ab^2 – b^3

The terms a^2b and ab^2 cancel each other out, resulting in:

a^3 – b^3 = a^3 – b^3

So, the final result is simply a^3 – b^3.

In summary, the formula (a^3 – b^3) = (a – b)(a^2 + ab + b^2) allows us to express the difference of two cubes in factored form.

 

Important Links

• http://licchavilyceum.com
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