Question

Geometrically explain the polynomial: $(2x+3{)}^2=4x^2+3^2+12x$

Answer 1

Step 1: Draw a line with a point which divides $2x,3$
Step 2: Total distance of this line $=2x+3$
Step 3: Now we have to find out the square of $2x+3$ i.e., Area of big square, $ABCD=$ $(2x+3{)}^2$
Step 4: From the diagram, inside square red and yellow square, be written as $4x^2,3^2$
Step 5: The remaining corner side will be calculated as rectangular side $=$ length $\times$ breadth $=$ $2x\times 3$
Therefore, Area of the big square, $ABCD=$ Sum of the inside square $+$ $2$ times the corner rectangular side.
$(2x+3{)}^2=4x^2+3^2+12x$
Hence, geometrically we proved the identity $(2x+3{)}^2=4x^2+3^2+12x$.