Ta có 4x²+8xy-3x-6y=4x(x+2y) -3(x+2y)=(x+2y)(4x-3)

4x²+8xy-3x-6y

=(4x²-3x)+(8xy-6y)

=x(4x-3)+2y(4x-3)

=(4x-3)(x+2y)

\(=\left(4x^2+8xy\right)-\left(3x+6y\right)\)
\(=4x.\left(x+2y\right)-3\left(x+2y\right)\)
\(=\left(x+2y\right).\left(4x-3\right)\)

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

\(4x^2+8xy+3x+6y\)

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

\(=7\left(x+2y\right)\)

=4x(x+2y)+3(x+2y)=(x+2y)(4x+3)

\(4x^2+8xy-3x-6y=4x\left(x+2y\right)-3\left(x+2y\right)=\left(4x-3\right)\left(x+2y\right)\)

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

\(x^3-5x^2-14x=x\left(x^2-5x-14\right)=x\left(x^2-7x+2x-14\right)=x\left[x\left(x-7\right)+2\left(x-7\right)\right]=x\left(x-7\right)\left(x+2\right)\)

\(x^4+4y^4=\left(x^2\right)^2+2\times x^2\times2y^2+\left(2y^2\right)^2-4x^2y^2=\left(x^2+2y^2\right)^2-\left(2xy\right)^2=\left(x^2-2xy+2y^2\right)\left(x^2+2xy+2y^2\right)\)

d) x(4x+3) -2y(4x+3)

=(4x+3)(x-2y)

e)x(x^2-9)-2(x^2-9)

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

f)= (x+1)^3

a) \(=\left(3ax+3bx\right)-\left(4by+4ay\right)=3x\left(a+b\right)-4y\left(a+b\right)=\left(a+b\right)\left(3x-4y\right)\)

b) \(=3\left[\left(x^2-2xy+y^2\right)-4t^2\right]=3\left[\left(x-y\right)^2-4t^2\right]=3\left(x-y-2t\right)\left(x-y+2t\right)\)

c) Không phân tích được

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

c)\(=\left(x-7\right)\left(x-1\right)\)

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

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

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

4x² - 9y² + 4x - 6y

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

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

\(4x^2-9y^2+4x-6y\)

\(=\left(4x^2+4x+1\right)-\left(9y^2+6y+1\right)\)

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

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

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

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

22, \(15x^2y+20xy^2-25xy=5xy\left(3x+4y-5\right)\)

23, \(4x^2+8xy-3x-6y=4x\left(x+2y\right)-3\left(x+2y\right)=\left(4x-3\right)\left(x+2y\right)\)

24, \(x^3-6x^2+9x=x\left(x^2-6x+9\right)=x\left(x-3\right)^2\)

Tương tự :)) 

21.\(x^3-4x^2+4x\)

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

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

22,\(15x^2y+20xy^2-25xy\)

\(=5xy\left(3x+4y-5\right)\)

23,\(4x^2+8xy-3x-6y\)

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

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

24\(x^3-6x^2+9x\)

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

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

25,\(x^2-xy+x-y\)

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

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

26.\(xy-2x-y^2+2y\)

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

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

27,\(x^2+x-xy-y\)

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

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

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

28,\(x^2+4x-y^2+4\)

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

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

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

29.\(x^2-2xy+y^2-4\)

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

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

1) 2x² - 4x = 2x( x - 2 )

2) 3x - 6y = 3( x - 2y )

3) x² - 3x = x( x - 3 )

4) 4x² - 6x = 2x( x - 3 )

5) x³ - 4x = x( x² - 4 ) = x( x - 2 )( x + 2 )

1) \(2x^2-4x=2x\left(x-2\right)\)

2) \(3x-6y=3\left(x-2y\right)\)

3) \(x^2-3x=x\left(x-3\right)\)

4) \(4x^2-6x=2x\left(2x-3\right)\)

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

1, \(2x^2-4x=2x\left(x-2\right)\)

2, \(3x-6y=3\left(x-2y\right)\)

3, \(x^2-3x=x\left(x-3\right)\)

4, \(4x^2-6x=2x\left(x-3\right)\)

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