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
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 )`
