Square of Sum / Difference Calculator
This calculator allows you to find the square of a sum (a + b)² or the square of a difference (a - b)² with step-by-step explanations.
Understanding Square of Sum and Difference
The square of a sum or difference is an algebraic identity:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
It is useful in algebra, expansion, factorization, and solving equations.
Example: (3 + 4)² → 3² + 2×3×4 + 4² = 9 + 24 + 16 = 49
Example: (5 - 2)² → 5² - 2×5×2 + 2² = 25 - 20 + 4 = 9
How the Calculator Works
The calculator automatically:
Step 1: Takes input values a and b
Step 2: Selects operation: square of sum or square of difference
Step 3: Applies the algebraic formula
Step 4: Displays result with step-by-step expansion
Examples
1. a = 3, b = 4, (a + b)² → 49
2. a = 5, b = 2, (a - b)² → 9
3. a = -3, b = 6, (a + b)² → 9
4. a = 7, b = 5, (a - b)² → 4
Why This Formula Matters
This identity simplifies algebraic expansions, helps in solving quadratic equations, and is widely used in geometry and algebra problem-solving.
Common Mistakes to Avoid
- Forgetting the middle term 2ab
- Misplacing the sign in (a - b)²
- Calculating each step incorrectly
Important: (a + b)² is not equal to a² + b² – always include 2ab.
Correct: Expand using (a ± b)² = a² ± 2ab + b².
Frequently Asked Questions
Can a and b be negative?
Yes. The formula works for positive and negative numbers.
Can I use decimals?
Yes. Decimal values are supported.
Does the order matter for (a - b)²?
Yes, (a - b)² ≠ (b - a)² in sign, but the value is the same because (a - b)² = (b - a)².
Conclusion
The square of sum and difference is a basic but powerful algebraic tool. This calculator quickly expands (a + b)² and (a - b)² with step-by-step results for any numbers.