Phân tích các đa thức sau thành nhân tử a) 10 (x-y)-5x (x-y) b) x^2-3x+xy-3y c) x^2+6x+9 d) 10x-25-x^2 f) 3x^2-3xy-5x+5y

Đáp án + Bước giải:

 `\text{a) 10(x – y) – 5x(x -y)}`

`\text{= 5(x – y)(2 – x)}`

`\text{b) x² – 3x + xy – 3y}`

`\text{= (x² + xy) – (3x + 3y)}`

`\text{= x(x + y) – 3(x + y)}`

`\text{= (x – 3)(x + y)}`

`\text{c) x² + 6x + 9}`

`\text{= x² + 3x + 3x + 9}`

`\text{= x(x + 3) + 3(x + 3)}`

`\text{= (x + 3)(x + 3) = (x + 3)²}`

`\text{d) 10x – 25 – x²}`

`\text{= -x² – 2.x.5 – 25}`

`\text{= -(x² + 2.x.5 + 5²)}`

`\text{= -(x + 5)²}`

`\text{f) 3x² – 3xy – 5x + 5y }`

`\text{= 3x(x – y) – 5(x – y)}`

`\text{= (3x – 5)(x – y)}`