a) \(6x^2-8x=2x\left(3x-4\right)\)
b) \(21x^2y^7-12x^5y^3=3x^2y^3\left(7y^4-4x^3\right)\)
c) \(4x^2y-6xy^2=2xy\left(2x-3y\right)\)
d) \(24x^2y-18xy^2=6xy\left(4x-3y\right)\)
e) \(9x^2y^2+12x^2y-15xy^2=3xy\left(3xy+4x-5y\right)\)
f) \(x\left(x+y\right)+y\left(-x-y\right)=x\left(x+y\right)-y\left(x+y\right)=\left(x+y\right)\left(x-y\right)\)
g) \(3\left(x+y\right)+x\left(x+y\right)=\left(x+y\right)\left(x+3\right)\)
h) \(3x\left(x-y\right)-6y\left(y-x\right)=3x\left(x-y\right)+6y\left(x-y\right)=3\left(x-y\right)\left(x+2y\right)\)
i) \(5x\left(x+1\right)-7x^2\left(x+1\right)=x\left(x+1\right)\left(5-7x\right)\)
j) \(6x^2\left(x-1\right)-10x\left(x-1\right)=2x\left(x-1\right)\left(3x-5\right)\)
k) \(5x\left(x+1\right)-7x^2\left(x+1\right)=x\left(x+1\right)\left(5-7x\right)\)
e) \(\left(x+2\right)\left(x+1\right)-\left(x+1\right)=\left(x+1\right)^2\)
e) 9x2y2+12x2y-15xy2=3xy(3x+4x-5y)
g)3(x+y)+x(x+y)=(3+x)(x+y)
h)3x(x-y)-6y(y-x)=(x-y)(3x-6y)