a: \(\left(2x^4-x^3+5x^{}-6x^2-1\right):\left(1-2x\right)\)

\(=\frac{2x^4-x^3-6x^2+5x-1}{-2x+1}\)

\(=\frac{-2x^4+x^3+6x^2-5x+1}{2x-1}=\frac{-x^3\left(2x-1\right)+6x^2-3x-2x+1}{2x-1}\)

\(=\frac{-x^3\left(2x-1\right)+3x\left(2x-1\right)-\left(2x-1\right)}{2x-1}=-x^3+3x-1\)

b: \(\left(x^3-3x^2+3x-2\right):\left(x^2-x+1\right)\)

\(=\frac{x^3-x^2+x-2x^2+2x-2}{x^2-x+1}\)

\(=\frac{x\left(x^2-x+1\right)-2\left(x^2-x+1\right)}{x^2-x+1}=x-2\)

c: \(\left(2x^3+5x^2-2x+3\right):\left(2x^2-x+1\right)\)

\(=\frac{2x^3-x^2+x+6x^2-3x+3}{2x^2-x+1}\)

\(=\frac{x\left(2x^2-x+1\right)+3\left(2x^2-x+1\right)}{2x^2-x+1}=x+3\)

d: \(\frac{5xy^2}{x^2y}+\frac{5y-x^2}{xy^2}\)

\(=\frac{y\cdot5xy^2+x\left(5y-x^2\right)}{x^2y^2}=\frac{5x^2y^2+5xy-x^3}{x^2y^2}=\frac{x\left(5xy^2+5y-x^2\right)}{x^2y^2}\)

\(=\frac{5xy^2+5y-x^2}{xy^2}\)

e: \(\frac{27-x^3}{5x^5}:\frac{2x-6}{3x^3}\)

\(=\frac{-\left(x-3\right)\left(x^2+3x+9\right)}{5x^5}\cdot\frac{3x^3}{2\left(x-3\right)}=\frac{-3\left(x^2+3x+9\right)}{5x^2\cdot2}=\frac{-3\left(x^2+3x+9\right)}{10x^2}\)

a) \(\frac{5\left(a-b\right)^3+2\left(a-b\right)^2}{\left(b-a\right)^2}=\frac{\left(a-b\right)^2\cdot\left[5\cdot\left(a-b\right)+2\right]}{\left(a-b\right)^2}=5\cdot\left(a-b\right)+2\)

b) \(\frac{5\left(x-2y\right)^3}{5x-10y}=\frac{5\left(x-2y\right)^3}{5\left(x-2y\right)}=\left(x-2y\right)^2\)

c) \(\frac{x^3+8y^3}{x+2y}=\frac{\left(x+2y\right)\left(x^2-2xy+4y^2\right)}{x+2y}=x^2-2xy+4y^2\)

a) \(\dfrac{\left(x+y\right)^2}{2}\)

b)\(\dfrac{5a-5b}{2}\)

c)\(\left(x-2y\right)^2\)

pt da thuc thanh nt ak bn

a,=x^2-[y-1]^2

=[x-y+1] [x+y-1]

b,=5[x-2y]-[x-2y].[x+2y]

=[x-2y].[5-x-2y]