Phân tích đa thức thành nhân tử:
a) \(7{x^2} - 28x + 28\) ;
b) \({x^2} - xy + x - y\) ;
c) \({a^2} - {b^2} - 5a + 5b\) ;
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d) \({x^2} - 6xy - 25 + 9{y^2}\) ;
e) \(49 - {y^2} - {x^2} + 2xy\).
\(\eqalign{ & a)\,\,7{x^2} - 28x + 28 = 7\left( {{x^2} - 4x + 4} \right) \cr & \,\,\,\,\, = 7\left( {{x^2} - 2.x.2 + {2^2}} \right) = 7{\left( {x - 2} \right)^2} \cr & b)\,\,{x^2} - xy + x - y = \left( {{x^2} - xy} \right) + \left( {x - y} \right) \cr & \,\,\,\,\, = x\left( {x - y} \right) + \left( {x - y} \right)\, = \left( {x - y} \right)\left( {x + 1} \right) \cr & c)\,\,{a^2} - {b^2} - 5a + 5b = \left( {{a^2} - {b^2}} \right) - \left( {5a - 5b} \right) \cr & \,\,\,\,\, = \left( {a - b} \right)\left( {a + b} \right) - 5\left( {a - b} \right) = \left( {a - b} \right)\left( {a + b - 5} \right) \cr & d)\,\,{x^2} - 6xy - 25 + 9{y^2} = \left( {{x^2} - 6xy + 9{y^2}} \right) - 25 \cr & \,\,\,\,\, = \left[ {{x^2} - 2.x.3y + {{\left( {3y} \right)}^2}} \right] - 25 = {\left( {x - 3y} \right)^2} - {5^2} \cr & \,\,\,\,\, = \left( {x - 3y - 5} \right)\left( {x - 3y + 5} \right) \cr & e)\,\,49 - {y^2} - {x^2} + 2xy = 49 - \left( {{y^2} + {x^2} - 2xy} \right) \cr & \,\,\,\,\, = {7^2} - {\left( {x - y} \right)^2} = \left( {7 - x + y} \right)\left( {7 + x - y} \right) \cr} \)