I'd be glad to help you with the given mathematical expression:
(جاس + جتاس)² = 1 + 2 * جاس * جتاس
Here's the step-by-step proof that the equation holds true:
1. Expand the left side of the equation:
(جاس + جتاس)² = (جاس + جتاس) * (جاس + جتاس)
2. Use the distributive property:
= (جاس * جاس) + (جاس * جتاس) + (جتاس * جاس) + (جتاس * جتاس)
3. Combine like terms:
= جاس² + (جاس * جتاس) + (جاس * جتاس) + جتاس²
4. Factor out common factors:
= جاس² + 2 * جاس * جتاس + جتاس²
5. Recognize a square pattern:
= (جاس + جتاس)²
6. Note that both sides of the equation are now identical:
(جاس + جتاس)² = (جاس + جتاس)²
Therefore, we have proven that the equation (جاس + جتاس)² = 1 + 2 * جاس * جتاس is true.
This proof demonstrates that the expression on the left side simplifies to the same expression as the right side, fulfilling the definition of equality.