`D = 4 (x^2 + x +1)^2 + 5x (x^2 + x + 1) + x^2`
` = [ 4 (x^2 + x + 1)^2 + 5x (x^2 +x + 1) + 25/16 x^2] - 9/16 x^2`
` = [ 2 (x^2 + x + 1)]^2 + 2 . 2 (x^2 + x + 1) . 5/4x + (5/4x)^2 - (3/4x)^2`
` = [ 2 (x^2 + x + 1) + 5/4x]^2 - (3/4x)^2`
`= (2x^2 + 2x + 2 + 5/4x)^2 - (3/4x)^2`
`= (2x^2 + 2x + 2 + 5/4x - 3/4x)(2x^2 + 2x + 2 + 5/4x + 3/4x)`
` = (2x^2 + 5/2x + 2)(2x^2 + 4x + 2)`
` = 2 (x^2 + 5/4x + 1) . 2 (x^2 + 2x + 1)`
` = 4 (x^2 + 5/4x + 1) (x^2 + 2x + 1)`
` = (4x^2 + 5x +4)(x+1)^2`
``
`F = (x+2)(x-4)(x+6)(x-12) + 36x^2`
` = [ (x+2)(x-12)] . [ (x-4)(x+6)] + 36x^2`
` = (x^2 - 12x + 2x - 24)(x^2 + 6x - 4x -24) +36x^2`
` = (x^2 - 10x - 24)(x^2 +2x - 24) + 36x^2`
Đặt `x^2 - 4x - 24 = t`
Khi đó ta có :
`F = (t - 6x)(t + 6x) + 36x^2`
` = t^2 - (6x)^2 + 36x^2`
` = t^2 - 36x^2 + 36x^2`
` = t^2`
Mà `t = x^2 - 4x - 24`
`=> F = (x^2 - 4x-24)^2`