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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