a. 16xy² - 12xy + 24x²y

= 4xy(4y - 3 + 6x)

c. 16 - x² + 2xy - y²

= 4² - (x² - 2xy + y²)

= 4² - (x - y)²

= (4 - x + y)(4 + x - y)

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

d: \(x^2-x-20=\left(x-5\right)\left(x+4\right)\)

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

a)5x²-5x+xy-y=(5x²-5x)+(xy-y)=5x(x-1)+y(x-1)=(x-1)(5x+y)

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

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

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

\(=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-2-z\right)\left(x-2+z\right)\)

\(x^2-2xy+y^2-z^2+10z-25\)

\(=\left(x-y\right)^2-\left(z-5\right)^2\)

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

a. x³ - 4x² + 4x - xz²

= x(x² - 4x + 4 ) - z²

= x(x - 4)² - z²

=x( x - 4 - z ) ( x - 4 + z )

b. x² - 2xy +y² - z² + 10z - 25

= ( x - y )² -  ( z - 5 )²

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

\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)

c: =(x-5)(x+3)

e: =(x+1-y)(x+1+y)

a) (x³-x²)+(8x-8)=x(x-1)+8(x-1)=(x²+8)(x-1)

b) 8x³-8x²y+2xy²=2x(4x²-4xy+y²)

c) (x²+y²-z²)² - 4x²y²=(x²+y²-z²)² - (2xy)²=(x²+y²-z²-2xy)(x²+y²-z²+2xy)

a) \(x^2-xy+x-y\)

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

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

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

b) \(x^2+2xy-4x-8y\)

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

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

c) \(x^3-x^2-x+1\)

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

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

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

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

=(x-2)(y+2)

b: \(=\left(x+y\right)^2-4\)

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

a.

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

\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)

\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)

b.

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

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

c.

\(=x^4-1+4x^2-4\)

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

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

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

a) Ta có: \(x^3+3x^2+3x+1-27z^3\)

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

\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)

b) Ta có: \(x^2-2xy+y^2-zx+yz\)

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

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

c) Ta có: \(x^4+4x^2-5\)

\(=x^4+4x^2+4-9\)

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

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

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

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

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

`c, (x+y)^2 - 2(x+y)z + z^2`

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