• Why does zero factorial (0!) equal 1 ?

Because there is

**exactly one**way to do nothing.
• How (a+b)

^{2}= a^{2}+ 2ab + b^{2}?
We can prove it geometrically.

Step 1: Draw a line of length (a + b)

a b

–––|––––––––––Step 2: Let's draw a square having sides of length (a + b). Area of this square will calculate the value of

(a+b)

^{2}.

This is a square consisting two rectangular and two square parts.

Area of square part 1 = a

^{2}

Area of rectangular part 2 = ab

Area of rectangular part 3 = ab

Area of square part 4 = b

^{2}

So, Area of square of length (a+b) = (a+b)

^{2 }= a

^{2}+ 2ab + b

^{2}

i.e. (a+b)

^{2 }= a

^{2}+ 2ab + b

^{2}

Hence Proved.