Phân tích thành nhân tử
a. \({x^4} + 2{x^3} + {x^2}\)
b. \({x^3} - x + 3{x^2}y + 3x{y^2} + {y^3} - y\)
c. \(5{x^2} - 10xy + 5{y^2} - 20{z^2}\)
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a. \({x^4} + 2{x^3} + {x^2}\) \( = {x^2}\left( {{x^2} + 2x + 1} \right) = {x^2}{\left( {x + 1} \right)^2}\)
b. \({x^3} - x + 3{x^2}y + 3x{y^2} + {y^3} – y\)
\(\eqalign{ & = \left( {{x^3} + 3{x^2}y + 3x{y^2} + {y^2}} \right) - \left( {x + y} \right) = {\left( {x + y} \right)^3} - \left( {x + y} \right) \cr & = \left( {x + y} \right)\left[ {{{\left( {x + y} \right)}^2} - 1} \right] = \left( {x + y} \right)\left( {x + y + 1} \right)\left( {x + y - 1} \right) \cr} \)
c. \(5{x^2} - 10xy + 5{y^2} - 20{z^2} = 5\left( {{x^2} - 2xy + {y^2} - 4{z^2}} \right)\)
\(\eqalign{ & = 5\left[ {\left( {{x^2} - 2xy + {y^2}} \right) - 4{z^2}} \right] = 5\left[ {{{\left( {x - y} \right)}^2} - {{\left( {2z} \right)}^2}} \right] \cr & = 5\left( {x - y + 2z} \right)\left( {x - y - 2z} \right) \cr} \)