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a) \(\Rightarrow x^3-3x^2+3x-1+3x^2-12x+1=0\)
\(\Rightarrow x^3-9x=0\)
\(\Rightarrow x\left(x-3\right)\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)
b) \(\Rightarrow x^3-1=x^3-9x^2+2x^2+6\)
\(\Rightarrow7x^2=7\)
\(\Rightarrow x^2=1\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
\(1,\\ a,=x^3-5x\\ b,=3x^3y-6x^3y^2+9xy\\ c,=6x^2-6x-36\\ d,=x^3+2x^2y-3xy^2\\ 2,\\ a,=4x^2-25\\ b,=x^2-6x+9\\ c,=9x^2+24x+16\\ d,=x^3-6x^2y+12xy^2-8y^3\\ e,=125x^3+225x^2y+135xy^2+27y^3\\ f,=125-x^3\)
\(g,=8y^3+x^3\\ 3,\\ a,=x\left(x+2\right)\\ b,=\left(x-3\right)^2\\ c,=\left(x-y\right)\left(y+5\right)\\ d,=2x\left(y+1\right)-y\left(y+1\right)=\left(2x-y\right)\left(y+1\right)\\ e,=6x^2y^2\left(xy^2+2y-3x\right)\)
\(a,\Leftrightarrow2x\left(x-3\right)\left(x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\\ b,\Leftrightarrow\left(2x-1\right)\left(x-2021\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=2021\end{matrix}\right.\\ c,\Leftrightarrow4x\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\\ d,\Leftrightarrow\left(3x+7-x-1\right)\left(3x+7+x+1\right)=0\\ \Leftrightarrow\left(2x+6\right)\left(4x+8\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-2\end{matrix}\right.\)
p) \(x^3-3x^2+3x-1+2\left(x^2-x\right)\\ =\left(x^3-1\right)-\left(3x^2-3x\right)+2x\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)-3x\left(x-1\right)+2x\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x+1-3x+2x\right)\\ =\left(x-1\right)\left(x^2+1\right)\)
p:Ta có: \(x^3-3x^2+3x-1+2\left(x^2-x\right)\)
\(=\left(x-1\right)^3+2x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-2x+1+2x\right)\)
\(=\left(x-1\right)\left(x^2+1\right)\)
\(a,\Rightarrow x^3-3x^2+3x-1+3x^2-12x+1=0\\ \Rightarrow x^3-9x=0\\ \Rightarrow x\left(x-3\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\\ b,\Rightarrow x^3-1=x^3-9x^2+2x^2+6\\ \Rightarrow7x^2=7\Rightarrow x^2=1\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Cảm ơn rất nhìu ạ