Math Problem Statement
•(〖n-1)〗^2- ((n-2)(n-1))/2 =(n-1)n/2 explain how answer came out and also factor out common factor
Solution
Let's solve and explain how the given expression:
Step by step:
1. Simplify the left-hand side expression
We begin by simplifying the left-hand side (LHS) step by step.
Expression:
First term:
Expand the square:
Second term:
First, expand : Now divide this by 2:
Now, substitute the expanded forms back into the expression:
2. Combine the terms
To combine these two terms, let's rewrite the first part as a fraction with the same denominator (2):
Now, subtract the numerators:
Expand and simplify:
So:
So, the simplified left-hand side is:
3. Right-hand side
The right-hand side of the equation is already given as:
4. Conclusion
Since the left-hand side equals the right-hand side, the equation is correct:
Factor out the common factor:
We see that already has as a common factor in the numerator, so this is the factored form of the final answer.
Summary:
- Expanded and simplified each term.
- Combined them under a common denominator.
- Simplified the final expression, showing it matches the right-hand side.
Would you like more details or further clarification?
Here are 5 relative questions for deeper understanding:
- How do you expand binomials like ?
- What is the process of combining fractions with different terms?
- How can common factors be identified in polynomial expressions?
- What steps are involved in factoring quadratic expressions?
- How does factoring simplify solving equations?
Tip: When dealing with fractions, always try to get a common denominator to simplify complex expressions easily.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Expansion
Simplification of Expressions
Formulas
(a-b)^2 = a^2 - 2ab + b^2
Multiplying binomials
Factoring out common terms
Theorems
Binomial Expansion Theorem
Distributive Property
Suitable Grade Level
Grades 9-12
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