Question

Devivation of: (a±b) 3 Formula: We know that: (a+b) 2 = a2 + 2ab +b 2 How??? (a+b) 2 = (a+b) (a+b) = a( a+b) + b(a+b) = a2 + ab + ab + b2 = a2 + 2ab + b2 (i) Hence, (a+b) 2= a2+2ab + b2...................................(i) (a+b)3 =?? Similarly: (a+b)3 = (a+b) (a+b)2 = (a+b) (a 2 + 2ab + b2 ) = a(a 2 + 2 ab + b2 ) + b(a 2 + 2 ab + b2 ) = a3+2a2b+ab2 + a 2b + 2ab2+ b3 = a 3+ 3a 2b + 3 ab2+ b3 So, (a+b)3= a 3+ 3a 2b + 3 ab2+ b3...................................(ii) OR, (ii) (a+b)3= a 3+ 3ab (a+b) + b3 [From (ii), 3ab is taken common from 2nd and 3rd term] ...................................(iii) Similarly: (a-b)3= a 3 - 3a 2b + 3ab2 -b 3......................................(iV) OR, (ii) (a-b)3= a 3 -3ab(a-b) - b 3 [From (iv), 3ab is taken common from 2nd and 3rd term]

Answer 1

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Answer 2

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