Cách 1: Tách một hạng tử thành tổng hai hạng tử để xuất hiện nhân tử chung.

a) x2 – 3x + 2

= x2 – x – 2x + 2 (Tách –3x = – x – 2x)

= (x2 – x) – (2x – 2)

= x(x – 1) – 2(x – 1) (Có x – 1 là nhân tử chung)

= (x – 1)(x – 2)

Hoặc: x2 – 3x + 2

= x2 – 3x – 4 + 6 (Tách 2 = – 4 + 6)

= x2 – 4 – 3x + 6

= (x2 – 22) – 3(x – 2)

= (x – 2)(x + 2) – 3.(x – 2) (Xuất hiện nhân tử chung x – 2)

= (x – 2)(x + 2 – 3) = (x – 2)(x – 1)

b) x2 + x – 6

= x2 + 3x – 2x – 6 (Tách x = 3x – 2x)

= x(x + 3) – 2(x + 3) (có x + 3 là nhân tử chung)

= (x + 3)(x – 2)

c) x2 + 5x + 6 (Tách 5x = 2x + 3x)

= x2 + 2x + 3x + 6

= x(x + 2) + 3(x + 2) (Có x + 2 là nhân tử chung)

= (x + 2)(x + 3)

Cách 2: Đưa về hằng đẳng thức (1) hoặc (2)

a) x2 – 3x + 2

(Vì có x2 và  nên ta thêm bớt  để xuất hiện HĐT)

= (x – 2)(x – 1)

b) x2 + x - 6

= (x – 2)(x + 3).

c) x2 + 5x + 6

= (x + 2)(x + 3).

a: =x(x-5)

a) \(=x\left(x-5\right)\)

b) \(=\left(x+3y-3y\right)\left(x+3y+3y\right)=x\left(x+6y\right)\)

c) \(=x\left(x+y\right)-3\left(x+y\right)=\left(x+y\right)\left(x-3\right)\)

b,=(x+3y-3y(x+3y+3y)

= x(x+6y)

a) (x - 2)(x - 3).                        b) 3(x - 2)(x + 5).

c) (x - 2)(3x + 1).                     d) (x-2y)(x - 5y).

e) (x + l)(x + 2)(x - 3).             g) (x-1)(x + 3)( x 2  + 3).

h) (x + y - 3)(x - y + 1).

`@` `\text {Ans}`

`\downarrow`

`a)`

`6x^2 - 3xy`

`= 3x(2x - y)`

`b)`

Bạn ghi lại đầy đủ thông tin

`c)`

`x^2 - 5x + 6`

`= x^2 - 2x - 3x +6`

`= (x^2 - 2x) - (3x - 6)`

`= x(x - 2) - 3(x - 2)`

`= (x - 3)(x - 2)`

a: =3x*2x-3x*y

=3x(2x-y)

c: =x^2-2x-3x+6

=x(x-2)-3(x-2)

=(x-2)(x-3)

b: Bạn ghi đầy đủ đề nha bạn

\(1,=3xy\left(x^2+2xy+y^2\right)=3xy\left(x+y\right)^2\\ 2,=7xy\left(2x-3y+4xy\right)\\ 3,=\left(x-1\right)\left(x^2-4\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\\ 4,=\left(x-y\right)\left(10x+8\right)=2\left(5x+4\right)\left(x-y\right)\\ 5,=\left(b-c\right)\left(8a-6b\right)=2\left(4a-3b\right)\left(b-c\right)\\ 6,=\left(x-1\right)\left(x^2-16\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\\ 7,=x\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(x+5\right)\\ 8,=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\\ 9,=\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\\ 10,=\left(x-1\right)^2-4y^2=\left(x-2y-1\right)\left(x+2y-1\right)\)

a) (x - 1)(x - 2).                        b) 4(x - 2)(x - 7).

c) (x + 2)(2x +1).                    d) (x - l)(2x - 7).

e) (2x + 3y - 3)(2x - 3y +1).    g) (x - 3)( x 3   +   x 2  - x +1).

h) (x + y)(x + y-l)(x + y + l).

a) (x + 2)(x + 4).              b) 2(x + 6)(x + l).

c) 3(3x + 5)(x + l).           d) (6x -7y)(x + y).

a: \(x^2-9-x^2\left(x^2-9\right)\)

\(=\left(x^2-9\right)-x^2\left(x^2-9\right)\)

\(=\left(x^2-9\right)\left(1-x^2\right)\)

\(=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\)

b: \(x^2\left(x-y\right)+y^2\left(y-x\right)\)

\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)

\(=\left(x-y\right)\left(x^2-y^2\right)\)

\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)=\left(x-y\right)^2\cdot\left(x+y\right)\)

c: \(x^3+27+\left(x+3\right)\left(x-9\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)

\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)

\(=\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)

d: \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

\(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)

e: \(3x^2-4x-4\)

\(=3x^2-6x+2x-4\)

\(=3x\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(3x+2\right)\)

g: \(x^4+64y^4\)

\(=x^4+16x^2y^2+64y^4-16x^2y^2\)

\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)

\(=\left(x^2+8y^2-4xy\right)\left(x^2+8y^2+4xy\right)\)

h: \(a^2+b^2+2a-2b-2ab\)

\(=a^2-2ab+b^2+2a-2b\)

\(=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)

i: \(\left(x+1\right)^2-2\left(x+1\right)\left(y-3\right)+\left(y-3\right)^2\)

\(=\left(x+1-y+3\right)^2\)

\(=\left(x-y+4\right)^2\)

k: \(x^2\left(x+1\right)-2x\left(x+1\right)+\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)