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)

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

4x² - 4y²

= (2x)² - (2y)²

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

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

4x²-4y²=4.(x²-y²)=4.(x-y).(x+y)

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

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

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

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

Ta có: \(4x^2+12x+9\)

\(=4x^2+6x+6x+9\)

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

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

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

\(x^2+2xy-3x-6y\)

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

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

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