This document proves the formula (a+b)2 = a2 + b2 + 2ab using both geometric and algebraic approaches. Geometrically, it represents a+b as a line segment and draws the squares and rectangles that make up (a+b)2. Algebraically, it expands (a+b)2 using the distributive property and collects like terms. Both methods demonstrate that (a+b)2 equals the sum of the squares of a and b plus twice their product.

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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