Question

Derive the Equation → ( a + b )2

Answer 1

Let us calculate the area of a square

As you can see in the above figure,

The length of the square is

`L=(a+b)`

The width of the square is

`W=(a+b)`

Recall that the area of a square shape is given by

`A=L\cdot W`

So the area of the square becomes

`\begin{gathered} A=L\cdot W \\ A=(a+b)\cdot(a+b) \\ A=(a+b)^2 \end{gathered}`

Now let us draw the square again,

As you can see in the above figure,

The area of the square is

`\begin{gathered} A=a^2+ab+ab+b^2 \\ A=a^2+2ab+b^2 \end{gathered}`

Therefore,

`(a+b)^2=a^2+2ab+b^2`