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The Factors Of X3 −X2y − Xy2 + Y3 Are - Mathematics

MCQ

The factors of x3 −x2y − xy2 + y3 are

Options

  • (x + y) (x2 − xy + y2)

  • (x + y) (x2 + xy + y2)

  • (x + y)2 (x − y)

  • (x − y)2 (x + y)

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Solution

The given expression to be factorized is

 x3 −x2y − xy2 + y3 

Take common  `x^2` from the first two terms and `-y^2` from the last two terms. That is

 x3 −x2y − xy2 + y3 ` = x^2 (x-y) - y^2 (x-y)`

Finally, take common (x-y)from the two terms. That is

x3 −x2y − xy2 + y3  = `(x-y)(x^2 - y^2)`

                             ` = (x-y){(x)^2 - (y)^2 }`

                             ` = (x- y)(x+y)(x-y)`

                             ` = (x-y)^2 (x+y)`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Q 1 | Page 25
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