Mastering the Difference of Cubes: Simplify and Factorize Math Expressions

Difference of Cubes

The difference of cubes refers to the algebraic expression derived by subtracting two cubes

The difference of cubes refers to the algebraic expression derived by subtracting two cubes. More specifically, it refers to the difference between two perfect cubes, which are numbers raised to the power of 3.

The general form of the difference of cubes expression is:

a^3 – b^3

where ‘a’ and ‘b’ can be any real numbers.

To simplify the difference of cubes expression, we can use a special factoring formula, which states:

a^3 – b^3 = (a – b)(a^2 + ab + b^2)

In this formula, the first factor, (a – b), represents the difference between the two numbers being cubed. The second factor, (a^2 + ab + b^2), represents the sum of the squares of the two numbers and their product.

To understand this formula better, let’s go through an example:

Example:
Simplify the expression 8^3 – 2^3.

Using the difference of cubes formula, we have:
8^3 – 2^3 = (8 – 2)(8^2 + 8*2 + 2^2)
= (6)(64 + 16 + 4)
= 6(84)
= 504

So, the simplified expression is 504.

It’s important to note that the difference of cubes formula can also be used for more complex expressions involving variables. The key is to identify the cube terms and apply the formula accordingly.

I hope this explanation helps clarify the concept of the difference of cubes and how to simplify such expressions.

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