Question

$(2x+1)(2x+3)$ expand the identity geometrically.

Answer 1

Step 1: Draw a square and cut into $4$ parts.
Step 2: There are $4$ rectangle and $1$ square.
Step 3: Area of the full rectangle, $ABCD=$ $(2x+1)(2x+3)$
Step 4: Now we have to find the area of inside square and rectangle as shown in the figure.
Step 5: Consider the area of pink square $=$ $(2x{)}^2$ and the area of yellow rectangle $=$ length $\times$ breadth $=$ $6x$
Step 6: Area of blue rectangle $=$ $2x$ and the area of green rectangle $=$ $3$
Step 7: Area of full rectangle $=$ area of pink square $+$ area of yellow rectangle $+$ area of blue rectangle $+$ area of green rectangle.
i.e., $(2x+1)(2x+3)=(2x{)}^2+6x+2x+3$
$(2x+1)(2x+3)=(2x{)}^2+x(6+2)+3$
Hence, geometrically we expanded the identity $(2x+1)(2x+3)=(2x{)}^2+x(6+2)+3$.