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Question

(x+5)(x+6) expand the expansion geometrically.

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Solution

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= (x+5)(x+6)
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 = (x)2 and the area of yellow rectangle = length × breadth = 6x
Step 6: Area of blue rectangle = 5x and the area of green rectangle = 30
Step 7: Area of full rectangle = area of pink square + area of yellow rectangle + area of blue rectangle + area of green rectangle.
i.e., (x+6)(x+5)=(x)2+6x+5x+30
(x+6)(x+5)=(x)2+x(6+5)+30
Hence, geometrically we expanded the identity (x+6)(x+5)=(x)2+x(6+5)+30=x2+11x+30.
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