Phân tích các đa thức dau thành nhân tử bằng cách nhóm hạng tử a/ $x^{2}$ -3x+xy-3y b/ $x^{2}$ -2x- $4y^{2}$ -4y c/ $x^{3}$ + $2x^{2}$ +2x+1 d/ $x^{4}

`a) x^2 – 3x + xy – 3y`

`= (x^2 – 3x) + (xy – 3y)`

`= x(x – 3) + y(x – 3)`

`= (x + y)(x – 3)`

`b) x^2 – 2x – 4y^2 – 4y`
`= (x^2 – 4y^2) – (2x + 4y)`

`= [x^2 – (2y)^2)] – 2(x + 2y)`

`= (x – 2y)(x + 2y) – 2(x + 2y)`

`= (x + 2y)(x – 2y – 2)`

`c) x^3 + 2x^2 + 2x + 1`

`= x^3 + 2x^2. 1 + 2x. 1^2 + 1^3`

`= (x + 1)^3`

`d) x^4 – 2x^3 + 2x – 1`

`= (x^4 – 1) – (2x^3 – 2x)`

`= [(x^2)^2 – 1^2] – 2x(x^2 – 1)`

`= (x^2 – 1)(x^2 + 1) – 2x(x^2 – 1)`

`= (x^2 – 1)(x^2 + 1 – 2x)`

`e) x^6 – x^4 + 2x^3 + 2x^2`

`= (x^6 – x^4) + (2x^3 + 2x^2)`

`= x^4(x^2 – 1) + 2x^2(x + 1)`

`= x^4(x^2 – 1^2) + 2x^2(x + 1)`

`= x^4(x – 1)(x + 1) – 2x^2(x + 1)`

`= (x + 1)[x^4(x – 1) – 2x^2]`

`= (x + 1)(x^5 – x^4 – 2x^2)`

`f) x^2y + xy^2 + x^2z + y^2z + 2xyz`

`= x^2y + xy^2 + x^2z + xyz + y^2z + xyz`

`= (x^2y + xy^2) + (x^2z + xyz) + (y^2z + xyz)`

`= xy(x + y) + xz(x + y) + yz(y + x)`

`= (x + y)(xy + xz + yz)`