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Formula of cube

Formula of cube

  1. (a + b)3= a3+3a2b+3ab2+b3.
  2. (a + b)3 = a3 + b3 +3ab(a + b)

Proof of formula (2):

(a + b)3 = (a + b) (a + b)2

= (a + b) (a2 + 2ab + b2)

= a(a2 + 2ab + b2)+ b(a2 + 2ab + b2)

= a3 + 2a2 b + ab2+ a2b+2ab2+b3

= a3 + 3a2 b +3ab2 +b3

= a3 + b3 +3ab(a+b)

  1. (a – b)3= a3-3a2b+3ab2-b3.
  2. (a + b)3 = a3 – b3 – 3ab(a – b)

Proof of formula (4):

(a – b)3 = (a – b) (a – b)2

= (a – b) (a2 – 2ab + b2)

= a(a2 – 2ab + b2)- b(a2 – 2ab + b2)

= a3 – 2a2 b + ab2– a2b+2ab2-b3

= a3 – 3a2 b +3ab2 – b3

= a3 – b3 -3ab(a – b).

  1. a3 + b3 = (a + b) (a2 – ab + b2)
  2. a3 – b3 = (a – b) (a2 + 2ab + b2)

 

 

Corollary:

  1. a3 + b3 = (a + b)3– 3ab(a + b)
  2. a3 – b3 = (a – b)3+ 3ab(a – b).

 

 

 

 

 

 

 

 

 

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