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The factors of x^3-x^2y-x y^2+y^3 are (a...

The factors of `x^3-x^2y-x y^2+y^3` are (a`(x+y)(x^2-x y+y^2)` (b) `(x+y)(x^2+x y+y^2)` (c)`(x+y)^2(x-y)` (d) `(x-y)^2(x+y)`

Text Solution

Verified by Experts

Correct option is (D)
`x^3-x^2y-x y^2+y^3`
`=x^2(x-y)-y^2(x-y)`
`=(x-y)\(x+y)\(x-y)`
`=(x-y)^2\(x+y)`
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Knowledge Check

  • The following steps are involved in the factorisation of x^(2) (x - y) + (y-x) y^(2) . Arrange them in sequential order from the first to the last . (A) (x-y) [x^(2) - y^(2)] (B) x^(2)(x-y) - ( x- y) y^(2) (C) (x-y)^(2) (x + y) (D) (x-y) [(x + y)( x-y)]

    A
    ABDC
    B
    BADC
    C
    ABCD
    D
    CDAB

  • The value of (x + y)/(x - y) + (x - y)/(x + y) - (2(x^2 - y^2))/(x^2 - y^2) is :

    A
    `1`
    B
    `x`
    C
    `y`
    D
    `0`

  • (x + 2) (x + 1) = (x -2) (x -3) (y+3)(y+2)=(y-1)(y-2)

    A
    `x gt y`
    B
    ` x lt y`
    C
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    D
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