\(a,\left(5x^2-2xy+y^2\right)-\left(4x^2+y^2\right)+\left(x^2-5xy-1\right)\)
\(=5x^2-2xy+y^2-4x^2-y^2+x^2-5xy-1\)
\(=\left(5x^2-4x^2+x^2\right)+\left(-2xy-5xy\right)+\left(y^2-y^2\right)-1\)
\(=2x^2-7xy-1\)
\(b,-5x^2y^4\left(3x^3y^2-2x^2y^3-xy\right)\)
\(=-5x^2y^4\cdot3x^3y^2+\left(-5x^2y^4\right)\cdot\left(-2x^2y^3\right)+\left(-5x^2y^4\right)\cdot\left(-xy\right)\)
\(=-15x^5y^6+10x^4y^7+5x^3y^5\)
\(c,-2\left(2xy+1\right)\left(3x-2y\right)\)
\(=-2\left[2xy\left(3x-2y\right)+\left(3x-2y\right)\right]\)
\(=-2\left(6x^2y-4xy^2+3x-2y\right)\)
\(=-12x^2y+8xy^2-6x+4y\)
\(d,\left(12x^3y^4+\dfrac{1}{2}x^3y^5-2x^5y^3\right):\left(-3x^3y^3\right)\)
\(=12x^3y^4:\left(-3x^3y^3\right)+\dfrac{1}{2}x^3y^5:\left(-3x^3y^3\right)+\left(-2x^5y^3\right):\left(-3x^3y^3\right)\)
\(=-4y-\dfrac{1}{6}y^2+\dfrac{2}{3}x^2\)
\(\text{#}\mathit{Toru}\)
