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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) \(\Rightarrow x^3-1=x^3-9x^2+2x^2+6\)
\(\Rightarrow7x^2=7\)
\(\Rightarrow x^2=1\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
\(a,\Rightarrow x^3-3x^2+3x-1+3x^2-12x+1=0\\ \Rightarrow x^3-9x=0\\ \Rightarrow x\left(x-3\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\\ b,\Rightarrow x^3-1=x^3-9x^2+2x^2+6\\ \Rightarrow7x^2=7\Rightarrow x^2=1\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
a: \(\left(x^2+1\right)\left(x-3\right)-\left(x-3\right)\left(x^2+3x+9\right)\)
\(=\left(x-3\right)\left(x^2+1-x^2-3x-9\right)\)
=(x-3)(-3x-8)
b: \(\left(x+2\right)^2+x\left(x+5\right)\)
\(=x^2+4x+4+x^2+5x\)
\(=2x^2+9x+4=2x^2+8x+x+4\)
=2x(x+4)+(x+4)
=(x+4)(2x+1)
c: \(\left(5x+4y\right)\left(5x-4y\right)-24x^2+15y^2\)
\(=25x^2-16y^2-24x^2+15y^2\)
\(=x^2-y^2=\left(x-y\right)\left(x+y\right)\)
\(1,\\ a,=x^3-5x\\ b,=3x^3y-6x^3y^2+9xy\\ c,=6x^2-6x-36\\ d,=x^3+2x^2y-3xy^2\\ 2,\\ a,=4x^2-25\\ b,=x^2-6x+9\\ c,=9x^2+24x+16\\ d,=x^3-6x^2y+12xy^2-8y^3\\ e,=125x^3+225x^2y+135xy^2+27y^3\\ f,=125-x^3\)
\(g,=8y^3+x^3\\ 3,\\ a,=x\left(x+2\right)\\ b,=\left(x-3\right)^2\\ c,=\left(x-y\right)\left(y+5\right)\\ d,=2x\left(y+1\right)-y\left(y+1\right)=\left(2x-y\right)\left(y+1\right)\\ e,=6x^2y^2\left(xy^2+2y-3x\right)\)
\(a,=\left(4x^2-1\right)\left(2x-5\right)=8x^3-20x^2-2x+5\\ b,=\left[x^2+\left(x-3\right)\right]\left[x^2-\left(x-3\right)\right]=x^4-\left(x-3\right)^2\\ =x^4-x^2+6x-9\)
b: Ta có: \(B=x^2\left(11x-2\right)+x^2\left(x-1\right)-3x\left(4x^2-x-2\right)\)
\(=11x^3-2x^2+x^3-x^2-12x^3+3x^2+6x\)
\(=6x\)