Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
a.6{x^2}{\rm{ }} - {\rm{ }}3xy{\rm{ }}\\
{\rm{ = 3x}}\left( {2x - y} \right)\\
b.{x^2} - {\rm{ }}{y^2} - {\rm{ }}6x{\rm{ }} + {\rm{ }}9{\rm{ }}\\
{\rm{ = }}\left( {{x^2} - 6x + 9} \right) - {y^2}\\
= {\left( {x - 3} \right)^2} - {y^2}\\
= \left( {x - 3 - y} \right)\left( {x - 3 + y} \right)\\
c.{x^2}{\rm{ }} + {\rm{ }}5x{\rm{ }} - {\rm{ }}6\\
= {x^2} - x + 6x - 6\\
= x\left( {x - 1} \right) + 6\left( {x - 1} \right)\\
= \left( {x - 1} \right)\left( {x + 6} \right)\\
{\rm{ }}d.{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} + {\rm{ }}2z} \right)^2} + {\rm{ }}{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} - {\rm{ }}z} \right)^2}{\rm{ }} - {\rm{ }}9{z^2}\\
= {\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} + {\rm{ }}2z} \right)^2} + {\rm{ }}{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} - {\rm{ }}z} \right)^2}{\rm{ }} - {\left( {3z} \right)^2}\\
= {\left( {x + y + 2z} \right)^2} + \left( {x + y - z - 3z} \right)\left( {x + y - z + 3z} \right)\\
= {\left( {x + y + 2z} \right)^2} + \left( {x + y - 4z} \right)\left( {x + y + 2z} \right)\\
= \left( {x + y + 2z} \right)\left( {x + y + 2z + x + y - 4z} \right)\\
= \left( {x + y + 2z} \right)\left( {2x + 2y - 2z} \right)\\
= 2\left( {x + y + 2z} \right)\left( {x + y - z} \right)
\end{array}\]

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Answer 2

\[\begin{array}{l}
a.6{x^2}{\rm{ }} - {\rm{ }}3xy{\rm{ }}\\
{\rm{ = 3x}}\left( {2x - y} \right)\\
b.{x^2} - {\rm{ }}{y^2} - {\rm{ }}6x{\rm{ }} + {\rm{ }}9{\rm{ }}\\
{\rm{ = }}\left( {{x^2} - 6x + 9} \right) - {y^2}\\
= {\left( {x - 3} \right)^2} - {y^2}\\
= \left( {x - 3 - y} \right)\left( {x - 3 + y} \right)\\
c.{x^2}{\rm{ }} + {\rm{ }}5x{\rm{ }} - {\rm{ }}6\\
= {x^2} - x + 6x - 6\\
= x\left( {x - 1} \right) + 6\left( {x - 1} \right)\\
= \left( {x - 1} \right)\left( {x + 6} \right)\\
{\rm{ }}d.{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} + {\rm{ }}2z} \right)^2} + {\rm{ }}{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} - {\rm{ }}z} \right)^2}{\rm{ }} - {\rm{ }}9{z^2}\\
= {\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} + {\rm{ }}2z} \right)^2} + {\rm{ }}{\left( {x{\rm{ }} + {\rm{ }}y{\rm{ }} - {\rm{ }}z} \right)^2}{\rm{ }} - {\left( {3z} \right)^2}\\
= {\left( {x + y + 2z} \right)^2} + \left( {x + y - z - 3z} \right)\left( {x + y - z + 3z} \right)\\
= {\left( {x + y + 2z} \right)^2} + \left( {x + y - 4z} \right)\left( {x + y + 2z} \right)\\
= \left( {x + y + 2z} \right)\left( {x + y + 2z + x + y - 4z} \right)\\
= \left( {x + y + 2z} \right)\left( {2x + 2y - 2z} \right)\\
= 2\left( {x + y + 2z} \right)\left( {x + y - z} \right)
\end{array}\]

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