Toán Lớp 8: x^2-Xy+x^3-3x^2y+3xy^2-y^3
3x^3-x^2-21x+7
x^3-4^2 +8x-8
x^3 -5x^2 -5x+1
x^2y- xz +z-y
x^4-x^3+x^2-1
x^4-x^2+10x-25
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Toán Lớp 8: x^2-Xy+x^3-3x^2y+3xy^2-y^3
3x^3-x^2-21x+7
x^3-4^2 +8x-8
x^3 -5x^2 -5x+1
x^2y- xz +z-y
x^4-x^3+x^2-1
x^4-x^2+10x-25
Comments ( 1 )
a){x^2} – xy + {x^3} – 3{x^2}y + 3x{y^2} – {y^3}\\
= x\left( {x – y} \right) + {\left( {x – y} \right)^3}\\
= \left( {x – y} \right)\left( {x + {{\left( {x – y} \right)}^2}} \right)\\
= \left( {x – y} \right) + ({x^2} + {y^2} + x – 2xy)\\
b)3{x^3} – {x^2} – 21x + 7\\
= {x^2}\left( {3x – 1} \right) – 7\left( {3x – 1} \right)\\
= \left( {3x – 1} \right)\left( {{x^2} – 7} \right)\\
c){x^3} – 4{x^2} + 8x – 8\\
= {x^3} – 4{x^2} + 4x + 4x – 8\\
= x\left( {{x^2} – 4x + 4} \right) + 4\left( {x – 2} \right)\\
= x{\left( {x – 2} \right)^2} + 4\left( {x – 2} \right)\\
= \left( {x – 2} \right)\left( {x\left( {x – 2} \right) + 4} \right)\\
= \left( {x – 2} \right)\left( {{x^2} – 2x + 4} \right)\\
d){x^3} – 5{x^2} – 5x + 1\\
= {x^3} + 1 – 5{x^2} – 5x\\
= \left( {x + 1} \right)\left( {{x^2} – x + 1} \right) – 5x\left( {x + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^2} – x + 1 – 5x} \right)\\
= \left( {x + 1} \right)\left( {{x^2} – 6x + 1} \right)\\
e){x^2}y – xz + z – y\\
= {x^2}y – y + z – xz\\
= y\left( {{x^2} – 1} \right) – z\left( {x – 1} \right)\\
= \left( {x – 1} \right)\left( {y.\left( {x + 1} \right) – z} \right)\\
= \left( {x – 1} \right)\left( {xy + y – z} \right)\\
f){x^4} – {x^3} + {x^2} – 1\\
= {x^3}\left( {x – 1} \right) + \left( {x – 1} \right)\left( {x + 1} \right)\\
= \left( {x – 1} \right)\left( {{x^3} + x + 1} \right)\\
g){x^4} – {x^2} + 10x – 25\\
= {x^4} – \left( {{x^2} – 10x + 25} \right)\\
= {x^4} – {\left( {x – 5} \right)^2}\\
= \left( {{x^2} – x + 5} \right)\left( {{x^2} + x – 5} \right)
\end{array}$