Algebraic Identity - Sum of Cubes


 
 
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Algebraic Identity - Sum of Cubes

Algebriac Identity- Sum of Cubes:

large a^3+b^3=(a+b)(a^2-ab+b^2)

To Prove this identity we simplify the right hand side as

large a^3+b^3=(a+b)(a^2-ab+b^2)

large a^3+b^3=a ;X; (a^2-ab+b^2);+;b;X;(a^2-ab+b^2)

large a^3+b^3= a^3-a^2b+ab^2+a^2b-ab^2+b^3

large a^3+b^3== a^3+b^3

For Example: Factorize large (3x)^3+(2y)^3

large (3x)^3+(2y)^3= (3x+2y)((3x)^2- 3x X 2y +(2y)^2)

large = (3x+2y)(9x^2- 6xy + 4y^2)

Sample Questions
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Question : 1

frac{(73)^3+(53)^3}{73X73-73X53+53X53}   =?

Right Option : A
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