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.