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\(3x\cdot\left(x-y\right)^2-6\cdot\left(y-x\right)\)
\(=3x\left(x-y\right)^2+6\left(x-y\right)\)
\(=\left(x-y\right)\left[3x\left(x-y\right)+6\right]\)
\(=\left(x-y\right)\left(3x^2-3xy+6\right)\)
\(x^2+x-6=x^2-2x+3x-6=x\left(x-2\right)+3\left(x-2\right)=\left(x-2\right)\left(x+3\right)\)
x2 + x - 6
= x2 - 2x + 3x - 6
= x ( x - 2 ) + 3 ( x - 2 )
= ( x - 2 ) ( x + 3 )
\(\left(x^3-2x^2\right)-\left(4x^2-8x\right)+\left(x-2\right).\)
\(x^2\left(x-2\right)-4x\left(x-2\right)+\left(x-2\right)\)
vậy................
\(\left(x^3-2x^2\right)-\left(4x^2-8x\right)+\left(x-2\right)\)
\(x^2\left(x-2\right)-4x\left(x-2\right)+\left(x-2\right)\)
Vậy ........
=(x-y-2y)[(x-y)^2+2y(x-y)+4y^2]
=(x-3y)(x^2-2xy+y^2+2xy-2y^2+4y^2)
=(x-3y)(x^2+3y^2)
\(\left(x-y\right)^3-8y^3\)
\(=\left(x-y\right)^3-\left(2y\right)^3\)
\(=\left[\left(x-y\right)-2y\right]\left[\left(x-y\right)^2+2y\left(x-y\right)+\left(2y\right)^2\right]\)
\(=\left(x-y-2y\right)\left(x^2-2xy+y^2+2xy-2y^2+4y^2\right)\)
\(=\left(x-3y\right)\left(x^2+3y^2\right)\)
\(\left(x-y\right)^3+\left(x+y\right)^3\\ =\left(x-y+x+y\right)\left(\left(x-y\right)^2-\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\right)\\ =2x\left(x^2-2xy+y^2-\left(x^2-y^2\right)+x^2+2xy+y^2\right)\\ =2x\left(x^2-2xy+y^2-x^2+y^2+x^2+2xy+y^2\right)\\ =2x\left(x^2+3y^2\right)\)
\(\left(x-y\right)^3-\left(x+y\right)^3\\ =\left(x-y-x-y\right)\left(\left(x-y\right)^2+\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\right)\\ =-2y\left(x^2-2xy+y^2+x^2-y^2+x^2+2xy+y^2\right)\\ =-2y\left(3x^2+y^2\right)\)
\(a^4-a^3-a^2+a\)
\(=a^3\left(a-1\right)-a\left(a-1\right)\)
\(=\left(a-1\right)\left(a^3-a\right)\)
=m^3-3m^2-3m^2+9n+2m-6
=m^2(m-3)-3m(m3)+2(m-3)
=(m-3)(m^2-3m+2)=(m-3)(m^2-m-2m+2)
=(m-3)[m(m-1)-2(m-1)]
=(m-3)(m-2)(m-1)
\(m^3-6m^2+11m-6\)
\(m^3-6m^2+11m-6\)
\(=\left(m-1\right)\left(m-3\right)\left(m-2\right)\)