Question

Geometrically verify the identity: $(x+y{)}^2=x^2+y^2+2xy$

Answer 1

Step 1: Draw a line with a point which divides $x,y$
Step 2: Total distance of this line $=x+y$
Step 3: Now we have to find out the square of $x+y$ i.e., Area of square $=$ $(x+y{)}^2$
Step 4: From the diagram, inside square red and yellow be written as $x^2,y^2$
Step 5: The remaining corner side will be calculated as rectangular side $=$ length $\times$ breadth = $x\times y$
Therefore, Area of the big square $=$ Sum of the inside square $+2$ times the corner rectangular side
$(x+y{)}^2=x^2+y^2+2xy$
Hence, geometrically we proved the identity $(x+y{)}^2=x^2+y^2+2xy$.