Question

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

Answer 1

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 )`