Math Problem Statement
factorise a ^ 3 + 1 / a ^ 3 + 2a + 2 / a
Solution
To factorize the expression , let's break it down step by step.
Step 1: Group the terms
The expression can be grouped as follows:
Step 2: Factorize each group
Notice that each group resembles a form that can be factored using algebraic identities.
- The first group can be recognized as a part of the identity for the sum of cubes. Using the identity:
But this identity simplifies better when combined with the second group.
- The second group can be factored as:
Step 3: Combine and factor further
Now, combine the factorizations from both groups:
We can factor out the common term :
Simplify the expression inside the brackets:
Final Factorized Form:
Thus, the factorized form of the expression is:
Would you like more details or have any questions?
Here are five related questions you might find helpful:
- How do you factorize expressions involving the difference of cubes?
- What are the key algebraic identities used in factorization?
- How do you simplify complex fractions like ?
- Can you factorize in a similar way?
- What is the importance of recognizing patterns in algebraic expressions?
Tip: Always check for common factors across terms before applying more complex factorization techniques.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factorization
Algebraic Identities
Formulas
Sum of cubes identity
Factorization of expressions involving fractions
Theorems
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Suitable Grade Level
Advanced High School