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Phân tích thành nhân tử:
a. \(5x – 5y + ax – ay\)
b. \({a^3} – {a^2}x – ay + xy\)
c. \(xy\left( {x + y} \right) + yz\left( {y + z} \right) + xz\left( {x + z} \right) + 2xyz\)
a. \(5x – 5y + ax – ay\) \( = \left( {5x – 5y} \right) + \left( {ax – ay} \right)\)
\( = 5\left( {x – y} \right) + a\left( {x – y} \right) = \left( {x – y} \right)\left( {5 + a} \right)\)
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b. \({a^3} – {a^2}x – ay + xy\) \( = \left( {{a^3} – {a^2}x} \right) – \left( {ay – xy} \right)\)
\( = {a^2}\left( {a – x} \right) – y\left( {a – x} \right) = \left( {a – x} \right)\left( {{a^2} – y} \right)\)
c. \(xy\left( {x + y} \right) + yz\left( {y + z} \right) + xz\left( {x + z} \right) + 2xyz\)
\(\eqalign{ & = {x^2}y + x{y^2} + yz\left( {y + z} \right) + {x^2}z + x{z^2} + xyz + xyz \cr & = \left( {{x^2}y + {x^2}z} \right) + yz\left( {y + z} \right) + \left( {x{y^2} + xyz} \right) + \left( {x{z^2} + xyz} \right) \cr & = {x^2}\left( {y + z} \right) + yz\left( {y + z} \right) + xy\left( {y + z} \right) + xz\left( {y + z} \right) \cr & = \left( {y + z} \right)\left( {{x^2} + yz + xy + xz} \right) = \left( {y + z} \right)\left[ {\left( {{x^2} + xy} \right) + \left( {xz + yz} \right)} \right] \cr & = \left( {y + z} \right)\left[ {x\left( {x + y} \right) + z\left( {x + y} \right)} \right] = \left( {y + z} \right)\left( {x + y} \right)\left( {x + z} \right) \cr} \)