a) \(\left(3x^2-6x+3x^3\right):3x\)
\(=\dfrac{3x^2-6x+3x^3}{3x}\)
\(=\dfrac{3x\left(x-2x+x^2\right)}{3x}\)
\(=x-2x+x^2\)
\(=-x+x^2\)
\(=-x\left(1-x\right)\)
a) \(=\left[3x\left(x-2+x^2\right)\right]:3x=x^2+x-2\)
b) \(=\left[5x^2y\left(x^4-5x^3y+2y\right)\right]:5x^2y=x^4-5x^3y+2y\)
c) \(=\left[2x^2\left(x^2-3\right)+x\left(x^2-3\right)+\left(x^2-3\right)\right]:\left(x^2-3\right)\)
\(=\left[\left(x^2-3\right)\left(2x^2+x+1\right)\right]:\left(x^2-3\right)=2x^2+x+1\)
d) \(=\left[x^2\left(2x-1\right)-4x\left(2x-1\right)+3\left(2x-1\right)\right]:\left(2x-1\right)\)
\(=\left[\left(2x-1\right)\left(x^2-4x+3\right)\right]:\left(2x-1\right)=x^2-4x+3\)
b) \(\left(5x^6y-25x^5y^2+10x^2y^2\right):5x^2y\)
\(=\dfrac{\left(5x^6y-25x^5y^2+10x^2y^2\right)}{5x^2y}\)
\(=\dfrac{5x^2y\left(x^4-5x^3y+2y\right)}{5x^2y}\)
\(=x^4-5x^3y+2y\)
