a: \(=15x^3y^2-x^3y^3+6x^2y^3\)
b: \(=x^2-4x+4+x^2-10x+25+2\left(5x-x^2-10+2x\right)\)
\(=2x^2-14x+29+2\left(-x^2+7x-10\right)\)
\(=2x^2-14x+29-2x^2+14x-20=9\)
c: \(=\dfrac{x^4-2x^3+3x^2+x^3-2x^2+3x}{x^2-2x+3}=x^2+x\)
a: \(3x^2y\left(5xy-\frac13xy^2+2y^2\right)\)
\(=3x^2y\cdot5xy-3x^2y\cdot\frac13xy^2+3x^2y\cdot2y^2\)
\(=15x^3y^2-x^3y^3+6x^2y^3\)
b: \(\left(x-2\right)^2+\left(5-x\right)^2+2\left(x-2\right)\left(5-x\right)\)
\(=\left(x-2+5-x\right)^2\)
\(=3^2=9\)
c: \(\left(x^4-x^3+x^2+3x\right):\left(x^2-2x+3\right)\)
\(=\left(x^4-2x^3+3x^2+x^3-2x^2+3x\right):\left(x^2-2x+3\right)\)
\(=x^2+x\)
