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Question

Verify (2p+q)2=4p2+q2+4pq geometrically.

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Solution

Step 1: Draw a line with a point which divides 2p,q
Step 2: Total distance of this line =2p+q
Step 3: Now we have to find out the square of 2p+q i.e., Area of big square, ABCD= (2p+q)2
Step 4: From the diagram, inside square red and yellow square, be written as 4p2,q2
Step 5: The remaining corner side will be calculated as rectangular side = length × breadth = 2p×q
Therefore, Area of the big square, ABCD= Sum of the inside square + 2 times the corner rectangular side.
(2p+q)2=4p2+q2+4pq
Hence, geometrically we proved the identity (2p+q)2=4p2+q2+4pq.
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