Verify $(2 p + q)^{2} = 4 p^{2} + q^{2} + 4 p q$ geometrically.

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Solution

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

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

Verify $(2 p + q)^{2} = 4 p^{2} + q^{2} + 4 p q$ geometrically.