$(x^2-x+2)(2x-3)$
$=2x^3-3x^2-2x^2+3x+4x-6$
$=2x^3-5x^2+7x-6$
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$(x^2-2xy-y^2)(x-y)$
$=(x-y)(x^2-2xy-y^2)$
$=x^3-2x^2y-xy^2-x^2y+2xy^2+y^3$
$=x^3-3x^2y+xy^2+y^3$
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$(x^2-3xy+y^5)(x+y)$
$=(x+y)(x^2-3xy+y^5)$
$=x^3-3x^2y+xy^5+x^2y-3xy^2+y^6$
$=x^3-2x^2y+xy^5-3xy^2+y^6$
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$(x-5)(x^2-6x+1)$
$=x^3-6x^2+x-5x^2+30x-5$
$=x^3-11x^2+31x-5$