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If AB+BA=0, then which of the following ...

If `AB+BA=0`, then which of the following is equivalent to `A^(3)-B^(3)`

A

`(A-B)(A^(2)+AB+B^(2))`

B

`(A-B)(A^(2)-AB-B^(2))`

C

`(A+B)(A^(2)-AB-B^(2))`

D

`(A+B)(A^(2)+AB-B^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(A+B)(A^(2)-AB-B^(2))=A^(3)-A^(2)B-AB^(2)+BA^(2)-BAB-B^(3)`
`=A^(3)-B^(3)-A^(2)B-AB^(2)-ABA+AB^(2)` ( `:' AB=-BA`)
`=A^(3)-B^(3)-A^(2)B+A^(2)B`
`=A^(3)-B^(3)`
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