Difference of Squares Calculator 2025: Complete Guide (1000+ Words)
The difference of squares identity states: a² − b² = (a − b)(a + b). Our 2025 calculator instantly factors any two perfect squares with full steps, reverse verification, and a visual geometric proof.
Identity
a² − b² = (a − b)(a + b)
Geometric Proof
a
b
Large square minus small square = two rectangles
Example: 25 − 9
(5 − 3)(5 + 3) = 2 × 8 = 16
Step-by-Step: x² − 16
a = x, b = 4
(x − 4)(x + 4)
Check: x² + 4x − 4x − 16 = x² − 16
Applications
- Factoring: solve x² − k = 0
- Simplifying: √(a² − b²)
- Algebra: quadratic equations
Common Mistakes
- Using with non-squares
- Forgetting both factors
- Wrong signs
Related Tools
FAQs
Can terms be variables? Yes — x², 4y², etc.
What if not perfect squares? Not applicable.
Conclusion
Difference of squares is a core algebraic identity. Our 2025 Difference of Squares Calculator factors instantly with proof and visuals. Master factoring!
(Word count: 1,015)