Question

Expand the polynomial geometrically: $y^2-7^2$

Answer 1

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