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The Factors Of X2 + 4y2 + 4y − 4xy − 2x − 8 Are - Mathematics

MCQ

The factors of x2 + 4y2 + 4y − 4xy − 2x − 8 are

Options

  • (x − 2y −4) (x − 2y + 2)

  • (x − y + 2) (x − 4y − 4)

  • (x + 2y − 4) (x + 2y + 2)

  • none of these

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Solution

The given expression to be factorized is  `x^2+ 4y^2 + 4y - 4xy - 2x - 8`

This can be arrange in the form

 x2 + 4y2 + 4y − 4xy − 2x − 8 ` = {x^2 - 4xy + 4y^2} -2 (x - 2y)-8`

` = {(x^2) -2.x.2y + (2y)^2} - 2 (x-2y)-2(x-2y)-8 `

` = (x -2y)^2 -2 (x-2y)-8`

Leta = (x -2y). Then the above expression becomes

`x^2 + 4y^2 + 4y -4xy -2x -8 = a^2 -2a - 8`

                                                      `= a^2 - (4 - 2)a -8`

                                                     ` = a^2 -4a+2a -8`

                                                     ` = a(a-4)+2 (a-4)`

                                                     `= (a-4 )(a+2)`

Put a = (x - 2y).

`x^2 + 4y^2 + 4y -4xy -2x -8 = {(x-2y) - 4}{(x-2y)+ 2}`

` = (x-  2y - 4)(x - 2y + 2 )`

  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 10 | Page 26
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