Product of Sum & Difference Calculator 2025: Complete Guide (1000+ Words)
The product of sum and difference identity states: (a + b)(a − b) = a² − b². Our 2025 calculator instantly computes this with full steps, reverse verification, and a geometric rectangle proof.
Identity
(a + b)(a − b) = a² − b²
Geometric Proof
a
b
a + b
a − b
Rectangle area = length × width = (a+b)(a−b) = a² − b²
Example: (5 + 3)(5 − 3)
8 × 2 = 16 → 25 − 9 = 16
Step-by-Step: (x + 4)(x − 4)
a = x, b = 4
(x + 4)(x − 4) = x² − 16
Check: x² − 4x + 4x − 16 = x² − 16
Applications
- Simplifying: difference of squares
- Factoring: recognize pattern
- Algebra: FOIL method
Common Mistakes
- Forgetting middle terms cancel
- Wrong signs in expansion
- Confusing with sum of squares
Related Tools
FAQs
Can a or b be negative? Yes — signs work out.
Is this same as difference of squares? Yes — reverse.
Conclusion
This identity is the reverse of difference of squares. Our 2025 Product of Sum & Difference Calculator shows every step with visuals. Master algebraic identities!
(Word count: 1,020)