The Factors of X3 − 1 + Y3 + 3xy Are - Mathematics

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MCQ

The factors of x3 − 1 + y3 + 3xy are

Options

  • (x − 1 + y) (x2 + 1 + y2 + x + y − xy)

  • (x + y + 1) (x2 + y2 + 1 −xy − x − y)

  •  (x − 1 + y) (x2 − 1 − y2 + x + y + xy)

  • 3(x + y −1) (x2 + y2 − 1)

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Solution

The given expression to be factorized is  x3 − 1 + y3 + 3xy 

This can be written in the form

 x3 − 1 + y3 + 3xy = `(x)^2 + (-1)^3 + (y)^3 -3 .(x).(-1).(y)`

Recall the formula  `a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)`

Using the above formula, we have 

x3 − 1 + y3 + 3xy 

` = {x+(-1)+ y}{(x)^2 + (-1)^2 + (y)^2 - (x).(-1) - (-1). (y) - (y).(x)}`

` = (x-1 + y)(x^2 + 1 + y^2 + x+ y -xy)`

So, the correct choice is (a).

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.6 [Page 25]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.6 | Q 2 | Page 25

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