• Why does zero factorial (0!) equal 1 ?
Because there is exactly one way to do nothing.
• How (a+b)2 = a2 + 2ab + b2 ?
We can prove it geometrically.
Step 1: Draw a line of length (a + b)
Step 2: Let's draw a square having sides of length (a + b). Area of this square will calculate the value of
This is a square consisting two rectangular and two square parts.
Area of square part 1 = a2
Area of rectangular part 2 = ab
Area of rectangular part 3 = ab
Area of square part 4 = b2
So, Area of square of length (a+b) = (a+b)2 = a2 + 2ab + b2
i.e. (a+b)2 = a2 + 2ab + b2