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Question

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Geometrically verify the identity: (x+y)

2

=x

2

+y

2

+2xy

Medium

Solution

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Step 1: Draw a line with a point which divides x,y

Step 2: Total distance of this line =x+y

Step 3: Now we have to find out the square of x+y i.e., Area of square = (x+y)

2

Step 4: From the diagram, inside square red and yellow be written as x

2

,y

2

Step 5: The remaining corner side will be calculated as rectangular side = length × breadth = x×y

Therefore, Area of the big square = Sum of the inside square +2 times the corner rectangular side

(x+y)

2

=x

2

+y

2

+2xy

Hence, geometrically we proved the identity (x+y)

2

=x

2

+y

2

+2xy.

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Answer:

Step-by-step explanation:

This is how (x+y)^2 = (x+y)*(x+y) = x(x+y) +y(x+y) = x^2 + xy + xy + y^2 = x^2 + y^2 + 2xy