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# Formulas for (a^3 – b^3) and (a^3 + b^3)

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Cubics are those intriguing mathematical expressions which involve the powers of three and can be extremely exhausting to solve sometimes. In this step-by-step guide, we’ll explain the formulas for (a3 – b3) and (a3 + b3) in an easy and approachable manner.

### Difference of Cubes (a3 – b3):

##### Step 1: Understand the Expression

Our journey begins with understanding the expression (a3 – b3).

##### Step 2: Recognize the Pattern

The formula for the difference of cubes is

a3 – b3 = (a – b)(a2 + ab + b2).

##### Step 3: Factorize

Now, let’s break down the expression into a product of a binomial and a trinomial:

(a – b)(a2 + ab + b2).

The difference of cubes is now neatly factorized.

Recommended Reading: What is the Derivative of sec x?

### Sum of Cubes (a3 + b3):

##### Step 1: Understand the Expression

Now, let’s explore (a3 + b3), this is the sum of two cubes.

##### Step 2: Recognize the Pattern

The formula for the sum of cubes is (a3 + b3 = (a + b)(a2 – ab + b2).

##### Step 3: Factorize

Just as we did before, break down the expression into a product of a binomial and a trinomial:

(a + b)(a2 – ab + b2).

The sum of cubes has now been transformed into a comprehensible and factorized form.

### Conclusion:

By recognizing the patterns and applying factorization magic, these seemingly complex cubic expressions have been demystified. Armed with these formulas, you’re well-equipped to tackle cubic challenges with confidence and ease. Keep exploring the fascinating world of mathematics!

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#### Moonpreneur

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