A)(x+y)^3-x^3-y^3 B) x^5-5x^3+4x C) x^3-11x^2+30x Phân tính da thuc thanh nhan tu

a) $(x+y)^3 - x^3 - y^3$

$= x^3 + 3x^2 + 3xy^2 + y^3 - x^3 - y^3$

$= 3x^2y + 3xy^2$

$= 3xy(x+y)$

b) $x(x^4 - 5x^2 + 4)$

$= x(x^2-1)(x^2-4)$

$=x(x-1)(x+1)(x-2)(x+2)$

$\begin{array}{l} a)\,\,\,{\left( {x + y} \right)^3} - {x^3} - {y^3}\\ \,\,\,\,\,\, = {x^3} + 3{x^2}y + 3x{y^2} + {y^3} - {x^3} - {y^3}\\ \,\,\,\,\,\, = \,3{x^2}y + 3x{y^2} = 3xy(x + y)\\ b)\,{x^5} - 5{x^3} + 4x\\ \,\,\,\,\, = x\left( {{x^4} - 5{x^2} + 4} \right) = x\left( {{x^4} - 4{x^2} - {x^2} + 4} \right)\\ \,\,\,\, = \,x\left[ {{x^2}\left( {{x^2} - 4} \right) - \left( {{x^2} - 4} \right)} \right] = x\left( {{x^2} - 1} \right)\left( {{x^2} - 4} \right)\\ \,\,\,\,\, = x(x - 1)(x + 1)(x - 2)(x + 2)\\ c)\,\,{x^3} - 11{x^2} + 30x\\ \,\,\,\,\, = \,\,x\left( {{x^2} - 11x + 30} \right) = x\left( {{x^2} - 5x - 6x + 30} \right)\\ \,\,\,\,\, = x\left[ {x(x - 5) - 6(x - 5)} \right]\\ \,\,\,\,\, = x(x - 5)(x - 6) \end{array}$