Algebraic Identity - Difference of Cubes


 
 
Concept Explanation
 

Algebraic Identity - Difference of Cubes

lgebriac Identity- Difference of Cubes:

large dpi{100} 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 (2a)^3-(3b)^3

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

large = (2a-3b)(4a^2- 6ab + 9b^2)

Sample Questions
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Question : 1

frac{(52)^3-(42)^3}{52X52+52X42+42X42}=?

Right Option : A
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Explanation
Question : 2

The factors of 1-p^{3} are _________________

Right Option : A
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Explanation
Question : 3

The value of  frac {(2.3)^3-0.027}{(2.3)^2+0.69+0.09}is

Right Option : A
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Explanation
 
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