Câu `1:`
`P = (x-y)^2 + (x+y)^2 - 2(x+y)(x-y) - 4x^2`
`= [ (x-y) - (x+y)]^2 - 4x^2`
`= (x-y - x-y)^2 - 4x^2`
` = (-2y)^2 - 4x^2`
`= 4y^2 - 4x^2`
Câu `2:`
`a)`
`x^3 - x^2y + 3x - 3y`
` = x^2 (x-y) + 3 (x-y)`
`= (x^2+3)(x-y)`
`b)`
`x^3 - 2x^2 - 4xy^2 + x`
`= x(x^2 - 2x - 4y^2 + 1)`
`= x [ (x^2 - 2x+1) - 4y^2]`
`= x [ (x-1)^2 - (2y)^2]`
` = x (x-1-2y)(x-1+2y)`
`c)`
`(x+2)(x+3)(x+4)(x+5) - 8`
` = [ (x+2)(x+5)] . [ (x+3)(x+4)] - 8`
`= (x^2 + 5x+2x+10)(x^2+4x+3x+12) - 8`
` = (x^2+7x+10)(x^2+7x+12)-8`
` = [ (x^2+7x+11) - 1] . [ (x^2+ 7x+11) + 1] - 8`
` = (x^2+ 7x+11)^2 - 1^2 - 8`
`= (x^2 + 7x+11)^2 - 9`
`= (x^2+7x+11)^2 - 3^2`
`= (x^2 + 7x + 11 - 3)(x^2 + 7x+11+3)`
` = (x^2 + 7x+8)(x^2 + 7x+14)`