2 . phân tích đa thức thành nhân tử a) x2 (y –z) +y2 (z-x) +z2 (x-y)
b) a2+b2¬-c2 -d2 -2ab -2cd
c) x4 – x3 – x2 +1
d) (x + y + z )3 – x3 – y3 – z3
e) x6-y6 f) x4 + 4×2 -5
g) x8 – 64×2
h) x12- 3x6y6+2y12
i) (x2-8)2 – 784
2 . phân tích đa thức thành nhân tử a) x2 (y –z) +y2 (z-x) +z2 (x-y)
b) a2+b2¬-c2 -d2 -2ab -2cd
c) x4 – x3 – x2 +1
d) (x + y + z )3 – x3 – y3 – z3
e) x6-y6 f) x4 + 4×2 -5
g) x8 – 64×2
h) x12- 3x6y6+2y12
i) (x2-8)2 – 784
\(\begin{array}{l}
a)\, = {x^2}y – {x^2}z + {y^2}z – {y^2}x + {z^2}\left( {x – y} \right)\\
= xy\left( {x – y} \right) – z\left( {{x^2} – {y^2}} \right) + {z^2}\left( {x – y} \right)\\
= \left( {x – y} \right)\left( {xy – zx – zy + {z^2}} \right)\\
= \left( {x – y} \right)\left( {x\left( {y – z} \right) – z\left( {y – z} \right)} \right)\\
= \left( {z – y} \right)\left( {x – z} \right)\left( {y – z} \right)\\
b)\, = {\left( {a – b} \right)^2} – {\left( {c + d} \right)^2}\\
= \left( {a – b + c + d} \right)\left( {a – b – c – d} \right)\\
c)\, = {x^3}\left( {x – 1} \right) – \left( {x – 1} \right)\left( {x + 1} \right)\\
= \left( {x – 1} \right)\left( {{x^3} – x – 1} \right)\\
d)\,\left( {y + z} \right)\left( {{{\left( {x + y + z} \right)}^2} + x\left( {x + y + z} \right) + {x^2}} \right) – \left( {y + z} \right)\left( {{y^2} – yz + {z^2}} \right)\\
= \left( {y + z} \right)\left( {3{x^2} + {y^2} + {z^2} + 3xy + 2yz + 3xz – {y^2} + yz – {z^2}} \right)\\
= \left( {y + z} \right)3\left( {{x^2} + xy + yz + xz} \right)\\
= 3\left( {y + z} \right)\left( {x\left( {x + y} \right) + z\left( {x + y} \right)} \right)\\
= 3\left( {y + z} \right)\left( {x + y} \right)\left( {x + z} \right)\\
e)\,{x^6} – {y^6} = \left( {{x^2} – {y^2}} \right)\left( {{x^4} + {x^2}{y^2} + {y^4}} \right)\\
= \left( {x – y} \right)\left( {x + y} \right)\left( {{x^4} + {x^2}{y^2} + {y^4}} \right)\\
f)\, = {x^4} + 5{x^2} – {x^2} – 5\\
= {x^2}\left( {{x^2} + 5} \right) – \left( {{x^2} + 5} \right)\\
= \left( {x – 1} \right)\left( {x + 1} \right)\left( {{x^2} + 5} \right)\\
g) = {x^2}\left( {{x^6} – 64} \right)\\
= {x^2}\left( {{x^3} – 8} \right)\left( {{x^3} + 8} \right)\\
= {x^2}\left( {x – 2} \right)\left( {{x^2} + 2x + 4} \right)\left( {x + 2} \right)\left( {{x^2} – 2x + 4} \right)\\
h)\, = {x^{12}} – 2{x^6}{y^6} – {x^6}{y^6} + 2{y^{12}}\\
= {x^6}\left( {{x^6} – 2{y^6}} \right) – {y^6}\left( {{x^6} – 2{y^6}} \right)\\
= \left( {{x^6} – 2{y^6}} \right)\left( {{x^6} – {y^6}} \right)\\
= \left( {{x^6} – 2{y^6}} \right){x^2}\left( {x – 2} \right)\left( {{x^2} + 2x + 4} \right)\left( {x + 2} \right)\left( {{x^2} – 2x + 4} \right)\\
i)\, = {\left( {{x^2} – 8} \right)^2} – {28^2}\\
= \left( {{x^2} + 20} \right)\left( {{x^2} – 36} \right)\\
= \left( {{x^2} + 20} \right)\left( {x – 6} \right)\left( {x + 6} \right)
\end{array}\)