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Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)=ax^2+a-xa^2-x=ax\left(x-a\right)-\left(x-a\right)=\left(x-a\right)\left(ax-1\right)\)
\(=x^2a+a-xa^2-x=x\left(xa-1\right)+a\left(1-xa\right)=\left(x-a\right)\left(xa-1\right)\)
\(=\left(6x^2-3x\right)+\left(4x-2\right)\)
\(=3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(3x+2\right)\left(2x-1\right)\)
\(=6x^2-3x+4x-2=6x\left(x-2\right)+2\left(x-2\right)=2\left(3x+2\right)\left(x-2\right)\)
a) \(3x^2-7x+2=3x^2-6x-x+2=3x\left(x-2\right)-\left(x-2\right)=\left(x-2\right)\left(3x-1\right)=\left(x-2\right)\left(x-\dfrac{1}{3}\right)\)
\(A=3x^2+6xy+3y^2-3z^2\)
\(=3\left(x^2+2xy+y^2-z^2\right)\)
\(=3\left[\left(x^2+2xy+y^2\right)-z^2\right]\)
\(=3\left[\left(x+y\right)^2-z^2\right]\)
\(=3\left(x+y+z\right)\left(x+y-z\right)\)
Làm
\(a,4m^2n-8mn^2-12n^2\)
\(=n\left(4m^2-8mn-12n\right)\)