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Question

Draw and expand the polynomial geometrically: (2x+y+z)2

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Solution

Step 1: Draw a square and cut into 9 parts.
Step 2: There are 3 squares (red, yellow, green) and 6 rectangles (2 pink, 2 purple, 2 blue)
Step 3: Area of the full square = (2x+y+z)2
Step 4: Now we have to find the area of 3 inside square(red, yellow, green) = (2x)2+y2+z2
Step 5: Consider the area of 2 pink rectangle = length × breadth = 2xy+2xy=4xy
Step 6: Area of 2 purple rectangle = 2xz+2xz=4xz and Area of 2 blue rectangle = yz+yz=2yz
Step 7: Area of full square = area of 3 inside square + area of 2 pink rectangle + area of 2 purple rectangle + area of 2 blue rectangle.
i.e., (2x+y+z)2=(2x)2+y2+z2+4xy+4xz+2yz
Hence, geometrically we expanded the identity (2x+y+z)2=(2x)2+y2+z2+4xy+4xz+2yz.
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