Let us calculate the area of a square
As you can see in the above figure,
The length of the square is
[tex]L=(a+b)[/tex]The width of the square is
[tex]W=(a+b)[/tex]Recall that the area of a square shape is given by
[tex]A=L\cdot W[/tex]So the area of the square becomes
[tex]\begin{gathered} A=L\cdot W \\ A=(a+b)\cdot(a+b) \\ A=(a+b)^2 \end{gathered}[/tex]Now let us draw the square again,
As you can see in the above figure,
The area of the square is
[tex]\begin{gathered} A=a^2+ab+ab+b^2 \\ A=a^2+2ab+b^2 \end{gathered}[/tex]Therefore,
[tex](a+b)^2=a^2+2ab+b^2[/tex]
