Question

Geometrically verify the identity: $(x+2y{)}^2=x^2+4y^2+4xy$

Answer 1

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