Toán Lớp 8: x^2 -y^2-x+y
3x^2(a+b+c)+36xy(a+b+c)+108y^2(a+b+c)
x^4+4x^2-5
x^3-19x-30
x^4+x^2+1
2x^3-5x^2+8x-3
3x^3-14x^2+4x+3
12x^2+5x-12y^2+12y-10xy-3
PHÂN TÍCH NHÂN TỬ
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Toán Lớp 8: x^2 -y^2-x+y
3x^2(a+b+c)+36xy(a+b+c)+108y^2(a+b+c)
x^4+4x^2-5
x^3-19x-30
x^4+x^2+1
2x^3-5x^2+8x-3
3x^3-14x^2+4x+3
12x^2+5x-12y^2+12y-10xy-3
PHÂN TÍCH NHÂN TỬ
Comments ( 1 )
+ {x^2} – {y^2} – x + y\\
= \left( {x – y} \right)\left( {x + y} \right) – \left( {x – y} \right)\\
= \left( {x – y} \right)\left( {x + y – 1} \right)\\
+ 3{x^2}\left( {a + b + c} \right) + 36xy\left( {a + b + c} \right) + 108{y^2}\left( {a + b + c} \right)\\
= 3\left( {a + b + c} \right)\left( {{x^2} + 12xy + 36{y^2}} \right)\\
= 3\left( {a + b + c} \right){\left( {x + 6y} \right)^2}\\
+ ){x^4} + 4{x^2} – 5\\
= {x^4} + 5{x^2} – {x^2} – 5\\
= \left( {{x^2} + 5} \right)\left( {{x^2} – 1} \right)\\
= \left( {{x^2} + 5} \right)\left( {x + 1} \right)\left( {x – 1} \right)\\
+ ){x^3} – 19x – 30\\
= {x^3} + 2{x^2} – 2{x^2} – 4x – 15x – 30\\
= \left( {x + 2} \right)\left( {{x^2} – 2x – 15} \right)\\
= \left( {x + 2} \right)\left( {x + 3} \right)\left( {x – 5} \right)\\
+ ){x^4} + {x^2} + 1\\
= {x^4} + 2{x^2} + 1 – {x^2}\\
= {\left( {{x^2} + 1} \right)^2} – {x^2}\\
= \left( {{x^2} + x + 1} \right)\left( {{x^2} – x + 1} \right)\\
+ )2{x^3} – 5{x^2} + 8x – 3\\
= 2{x^3} – {x^2} – 4{x^2} + 2x + 6x – 3\\
= \left( {2x – 1} \right)\left( {{x^2} – 2x + 3} \right)\\
+ )3{x^3} – 14{x^2} + 4x + 3\\
= 3{x^3} + {x^2} – 15{x^2} – 5x + 9x + 3\\
= \left( {3x + 1} \right)\left( {{x^2} – 5x + 3} \right)
\end{array}$
12{x^2} + 5x – 12{y^2} + 12y – 10xy – 3\\
= 12{x^2} – 18xy + 9x\\
– \left( {4x – 6y + 3} \right) + \left( {8xy – 12{y^2} + 6y} \right)\\
= 3x.\left( {4x – 6y + 3} \right) – \left( {4x – 6y + 3} \right)\\
+ 2y\left( {4x – 6y + 3} \right)\\
= \left( {4x – 6y + 3} \right)\left( {3x + 2y – 1} \right)
\end{array}$