Geometrical proof of (a+b)^2
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The document presents a geometrical proof for the formula (a + b)² = a² + 2ab + b². It illustrates the concept using area calculations of square and rectangular regions. The proof is attributed to Abdul Wasay Yusuf.
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Geometrical proof of (a+b)^2
- 1. A B CDIn the adjoining figure, m AE = mEH = a mEB = mFC = b mAB = mBC = a + b Geometrical Proof of formula (a + b)2 = a2 + 2ab + b2 E F GK H a b a b (a + b) a2 b2 ab ab Area of the square region ABCD = Area of square region AEHK( a2 ) + area of the square region HGCF( b2 ) + area of the rectangular region EBGH( ab ) + area of the rectangular region KHFD( ab ) i.e. (a+b)2= a2+b2+ab+ab = a2+2ab+b2 By: Abdul Wasay Yusuf