(x+a)^2=x^2+2ax+a^2 verify the equation by figure

You can prove it graphically. Start by drawing a large square with sides of length 'x+a.' Then see if you can sub-divide it into (a) a square with sides 'x', (b) two rectangles with sides 'x' and 'a', and (c) another square with sides 'a'. Then note that the sum of the areas of these four pieces equals the area of the original large square.