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

If a + b + c = 0 then :

Right Option : A
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Question : 2

Which of the following expression is a factor of large dpi{120} 343x^3-512 ?

Right Option : C
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Explanation
Question : 3

Which of the following expressions is the expansion of large a^3- b^3 ?

Right Option : A
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Explanation
 
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