Question

What is the geometrical expansion of the identity: $(12x+5)(12x+3)$?

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, $ABCD=$ $(12x+5)(12x+3)$
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 $=$ $(12x{)}^2$ and the area of yellow rectangle $=$ length $\times$ breadth $=$ $36x$
Step 6: Area of blue rectangle $=$ $60x$ and the area of green rectangle $=$ $15$
Step 7: Area of full rectangle $=$ area of pink square $+$ area of yellow rectangle $+$ area of blue rectangle $+$ area of green rectangle.
i.e., $(12x+5)(12x+3)=(12x{)}^2+36x+60x+15$
$(12x+5)(12x+3)=(12x{)}^2+x(36+60)+15$
Hence, geometrically we expanded the identity $(12x+5)(12x+3)=(12x{)}^2+x(36+60)+15$.