Why is (a+b)2 = a2+b2+2ab
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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.
Why is (a+b)2 = a2+b2+2ab
- 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. FreshersSite.com
- 2. Introduction to Geometrical Approach Line with a point = a+b a b a Square Area = a2 a a Rectangle Area = ab b FreshersSite.com
- 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 FreshersSite.com
- 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 FreshersSite.com