\(a,=x\left(2x-y\right)+\left(2x-y\right)=\left(x+1\right)\left(2x-y\right)\\ b,=\left(a+b\right)\left(c-2\right)\\ c,=x\left(x+4y\right)+2\left(x+4y\right)=\left(x+2\right)\left(x+4y\right)\\ d,=x\left(x+2y\right)+3\left(x+2y\right)=\left(x+3\right)\left(x+2y\right)\)

a) Cách 1.

Ta có 2xy + 3z + 6y + xz = (2xy + xz) + (3z + 6y)

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

Cách 2.

Ta có 2xy + 3z + 6y + xz = (2x1/ + 6y) + (3z + xz)

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

b) Biến đổi được a 4   -   9 rt 3   +   a 2 -9a = (a- 9)a( a 2  +1).

c) Biến đổi được 3 x 2  + 5y - 3xy + (-5x) = (x - y)(3x - 5).

d) Biến đổi được  x 2  - (a + b)x + ab = (x- a)(x - b).

e) Ta có 4 x 2 - 4xy + y 2   –   9 t 2 =  ( 2 x   -   y ) 2   -   ( 3 t ) 2

= (2x - y - 3t )(2x - y + 31).

g) Ta có  x 3   -   3 x 2 y   +   3 xy 2   -   y 3   -   z 3

= ( x   -   y ) 3   -   z 3 = (x - y - z)( x 2   +   y 2   +   z 2  - 2xy + xz - yz).

h) Ta có x 2   -   y 2 + 8x + 6y+ 7 = ( x 2  +8x + 16) - ( y 2  - 6y+ 9)

= ( x   +   4 ) 2   - ( y - 3 ) 2  =(x-y + 7)(x + y + l).

`9-x^2-2xy-y^2`

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

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

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

9-x²-2xy-y²=9-(x²+2xy+y²)=3²-(x+y)²=(3-x-y)(3+x+y)

a) Ta có: \(9-x^2-2xy-y^2\)

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

\(=\left(9-x-y\right)\left(9+x+y\right)\)

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

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

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

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

c) \(y^2+x^2+2xy-16=x^2+2xy+y^2-16\)

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

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

b) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+y+3\right)\left(x-y+3\right)\)

a) 3xy² - 3x³ - 6xy + 3x 

=3x (y² - x² - 2y +1)

= 3x [ (y-1)² -x² ]

=3x (y-1-x)(y-1+x)

b) 3x² +11x+6

= 3 x² +9x +2x +6

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

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

c) -x³ - 4xy² + 4x²y +16x

= -x (x² + 4y² - 4xy -16 )

= -x [(x -2y)² - 4² ]

= -x(x-2y-4)(x-2y+4) 

a) \(9x^2-16\)

\(=\left(3x\right)^2-4^2\)

\(=\left(3x-4\right)\left(3x+4\right)\)

b) \(x^2+4xy+4y^2-3x-6y\)

\(=\left(x^2+4xy+4y^2\right)-\left(3x+6y\right)\)

\(=\left[x^2+2\cdot x\cdot2y+\left(2y\right)^2\right]-3\left(x+2y\right)\)

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

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

#\(Toru\)

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

a) \(=3\left(x^2-8x+16\right)=3\left(x-4\right)^2\)

b) \(=5\left(x^2-1\right)=5\left(x-1\right)\left(x+1\right)\)

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

Bài 2:

a: =x(x^2-25)

=x(x-5)(x+5)

b: =x(x-2y)+3(x-2y)

=(x-2y)(x+3)

c: =(2x-3)(4x^2+6x+9)+2x(2x-3)

=(2x-3)(4x^2+8x+9)