CÂU3: Phân tích các đa thức sau thành nhân tử: a) x2 - y2 - 2x + 2y b) 2x + 2y - x2 - xy c) 3a2 - 6ab + 3b2 - 12c2 d) x2 - 25 + y2 + 2xy e) a2 + 2ab + b2 - ac - bc f) x2 - 2x - 4y2 - 4y g) x2y - x3 - 9y + 9x h) x2(x-1) + 16(1- x) n) 81x2 - 6yz - 9y2 - z2 m) xz-yz-x2+2xy-y2 p) x2 + 8x + 15 k) 81x4 + 4

Đáp án + Giải thích các bước giải:

 `a) x^2 - y^2 - 2x + 2y `

`= ( x^2 - y^2 ) - ( 2x - 2y ) `

`= ( x - y ) ( x + y ) - 2 ( x - y ) `

`= ( x - y ) ( x + y - 2 ) `

`b) 2x + 2y - x^2 - xy `

`= ( 2x + 2y ) - ( x^2 + xy ) `

`= 2 ( x + y ) - x ( x + y ) `

`= ( x + y ) ( 2 - x ) `

`c) 3a^2 - 6ab + 3b^2 - 12c^2 `

`= 3 ( x^2 - 2ab + b^2 - 4x^2 ) `

`= 3 [ ( a - b )^2 - (2c)^2 ] `

`= 3 ( a - b - 2c ) ( a - b + 2c ) `

`d) x^2 - 25 + y^2 + 2xy `

`= ( x^2 + 2xy + y^2 ) - 25 `

`= ( x + y )^2 - 5^2 `

`= ( x + y - 5 ) ( x + y + 5 ) `

`e) a^2 + 2ab + b^2 - ac - bc `

 `= ( a^2 + 2ab + b^2 ) - ( ac + bc ) `

`= ( a + b )^2 - c ( a + b ) `

`= ( a + b ) ( a + b - c ) `

`f) x^2 - 2x - 4y^2 - 4y `

`=  ( x^2 - 4y^2 ) - ( 2x + 4y ) `

`= ( x - 2y ) ( x + 2y ) - 2 ( x + 2y ) `

`= ( x + 2y ) ( x - 2y - 2 ) `

`g) x^2y - x^3 - 9y + 9x `

`= ( x^2y - 9y ) - ( x^3 - 9x ) `

`= y ( x^2 - 9 ) - x (x^2 - 9 ) `

`= ( x^2 - 9 ) ( y - x ) `

`= ( x - 3 ) ( x + 3 ) ( y - x )`

`h) x^2 ( x - 1 ) + 16 ( 1 - x ) `

`= x^2 ( x - 1 ) - 16 ( x - 1 ) `

`= ( x - 1 ) ( x^2 - 16 ) `

`= ( x - 1 ) ( x - 4 ) ( x + 4 ) `