Square of the Sum of Two Numbers

first number a

3

second number b

2

show

numbers

symbols

For any two numbers

a

and

b

the square of their sum

2

(a+b)

is equal to

2

a

+2ab+

2

b

. You can see a geometrical proof of this identity from the figure. The gray numbers represent the side lengths or areas of the entire figure and the black ones represent the side lengths or areas of the colored regions. Each set of numbers on the side or in the middle sums to the gray number.