\(a,=\left(2x-y\right)^2\\ b,=9x^2\left(x-y\right)-4\left(x-y\right)=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\\ c,=x^2+2+3x^2-6=4x^2-4=4\left(x-1\right)\left(x+1\right)\)

Lời giải:
a.

$x^2-7x+6=(x^2-x)-(6x-6)=x(x-1)-6(x-1)=(x-1)(x-6)$

b.

$x-3\sqrt{3}x-12\sqrt{3}$ không phân tích được thành nhân tử

c.

$x^2+4x-2$ không phân tích được thành nhân tử với các hệ số nguyên.

a) \(x^2+5x+4==x\left(x+1\right)+4\left(x+1\right)=\left(x+1\right)\left(x+4\right)\)

b) \(3x^2+4x-7=3x\left(x-1\right)+7\left(x-1\right)=\left(x-1\right)\left(3x+7\right)\)

c) \(x^2+7x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)

a) (x+1)(x+4)

b) (x-1)(3x+7)

c) (x+3)(x+4)

a) x²+5x+4 = x(x+4)+(x+4) = (x+4)(x+1)

b) 3x²+4x-7 = 3x(x-1)+7(x-1) = (x-1)(3x+7)

c) x²+7x+12 = x(x+4)+3(x+4) = (x+3)(x+4)

b) x²-3x+xy-3y

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

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

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

c) x²-y²-4x+4

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

=\(\left(x-2\right)^2\) \(-y^2\)

=(\(x-y-2\)) \(\left(x+y-2\right)\)

a)6x³y-9x²y²+3xy

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

\(a,4x-20y=4\left(x-5y\right)\\ b,10x^2+10xy-x-y=10x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(10x-1\right)\\ c,x^2-2xy-z^2+y^2=\left(x^2-2xy+y^2\right)-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

\(a,=4\left(x-5y\right)\\ b,=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\\ c,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

a) 4x - 20y

= 4 ( x - 5y )

b) 5x^2 + 5xy - x - y

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

= ( x + y ) ( 5x - 1 )

c) x^2 - 2xy - z^2 + y^2

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

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

= ( x - y + z ) ( x - y - z )

a) \(4\left(x-5y\right)\)

b) \(5x^2+5xy-x-y\)

\(=5x\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(5x-1\right)\)

c) \(x^2-2xy-z^2+y^2\)

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

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

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

c: =(x-2)(x-4)

b: \(=x\left(x^2+2xy+y^2-4\right)\)

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

\(a,4x^2-4x+1\\ =\left(2x\right)^2-2.2x+1^2=\left(2x-1\right)^2\\ c,x^2-6xy-25z^2+9y^2\\ =\left(x^2-2.x.3y+9y^2\right)-\left(5z\right)^2\\ =\left(x-3y\right)^2-\left(5z\right)^2\\ =\left(x-3y-5z\right)\left(x-3y+5z\right)\)

Xem lại đề ý b

\(3x^4y-12x^2y^3=3x^2y\left(x^2-4y^2\right)=3x^2y\left(x-2y\right)\left(x+2y\right)\)

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

\(x^3+3x^2+4x+12=x^2\left(x+3\right)+4\left(x+3\right)=\left(x^2+4\right)\left(x+3\right)\)

\(3x^2-6xy+3y^2-27=3\left[\left(x-y\right)^2-9\right]=3\left(x-y-3\right)\left(x-y+3\right)\)

Do câu d mình ko biết làm bởi v mình không làm được