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.
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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.
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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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