Prove (a+b)2=a2+b2+2ab in geometry and algebra.

1. This is the first formula we learn in
geometry, algebra of mathematics.
Lets find out why is this?
Here, we are going to prove how
(a+b) 2 = a 2+b2+2ab
in geometry and in algebra.
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2. Introduction to Geometrical Approach
 Line with a point = a+b
a b
a
 Square Area = a2
a
a
 Rectangle Area = ab
b
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3. Prove (a+b) 2 = a 2+b2+2ab in Geometry
 Draw a line with a point which divides a, b
a b
 Total distance of this line = a+b
 Now we have to find out the square of a+b ie. (a+b) 2
a b
a2 ab
ab b2
 The above diagram represents – a+b is a line and the
square are is a 2+b2+2ab
 Hence proved - (a+b) 2 = a 2+b2+2ab
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4. Prove (a+b) 2 = a 2+b2+2ab in Algebra
 (a+b) 2 = (a+b) *(a+b)
= (a*a + a*b) + (b *a + b*b)
= (a 2+ ab) + (ba + b2)
= a 2 + 2ab + b2
Hence proved
(a+b) 2 = a 2+b2+2ab
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