Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
a)(2x - y)(4{x^2} - 2xy + {y^2})\\
= 8{x^3} - 4{x^2}y + 2x{y^2} - 4{x^2}y + 2x{y^2} - {y^3}\\
= 8{x^3} - 8{x^2}y + 4x{y^2} - {y^3}\\
b)(6{x^5}{y^2} - 9{x^4}{y^3} + 15{x^3}{y^4}):3{x^3}{y^2}\\
= 3{x^3}{y^2}\left( {2{x^2} - 3xy + 5{y^2}} \right):3{x^3}{y^2}\\
= 2{x^2} - 3xy + 5{y^2}\\
c)(2{x^3} - 21{x^2} + 67x - 60):(x - 5)\\
= \left( {2{x^3} - 10{x^2} - 11{x^2} + 55x + 12x - 60} \right):\left( {x - 5} \right)\\
= \left[ {2{x^2}\left( {x - 5} \right) - 11x\left( {x - 5} \right) + 12\left( {x - 5} \right)} \right]:\left( {x - 5} \right)\\
= \left( {x - 5} \right)\left( {2{x^2} - 11x + 12} \right):\left( {x - 5} \right)\\
= 2{x^2} - 11x + 12\\
d)({x^4} + 2{x^3} + x - 25):({x^2} + 5)\\
= \left[ {{x^4} + 5{x^2} + 2{x^3} + 10x - 5{x^2} - 25 - 9x} \right]:\left( {{x^2} + 5} \right)\\
= \left[ {{x^2}\left( {{x^2} + 5} \right) + 2x\left( {{x^2} + 5} \right) - 5\left( {{x^2} + 5} \right) - 9x} \right]:\left( {{x^2} + 5} \right)\\
= \left( {{x^2} + 5} \right)\left( {{x^2} + 2x - 5} \right):\left( {{x^2} + 5} \right) - 9x:\left( {{x^2} + 5} \right)\\
= {x^2} + 2x - 5 - \frac{{9x}}{{{x^2} + 5}}\\
e)(27{x^3} - 8):(6x + 9{x^2} + 4)\\
= \left[ {{{\left( {3x} \right)}^3} - {2^3}} \right]:\left( {9{x^2} + 6x + 4} \right)\\
= \left( {3x - 2} \right)\left( {9{x^2} + 6x + 4} \right):\left( {9{x^2} + 6x + 4} \right)\\
= 3x - 2
\end{array}\]

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Answer 2

\[\begin{array}{l}
a)(2x - y)(4{x^2} - 2xy + {y^2})\\
= 8{x^3} - 4{x^2}y + 2x{y^2} - 4{x^2}y + 2x{y^2} - {y^3}\\
= 8{x^3} - 8{x^2}y + 4x{y^2} - {y^3}\\
b)(6{x^5}{y^2} - 9{x^4}{y^3} + 15{x^3}{y^4}):3{x^3}{y^2}\\
= 3{x^3}{y^2}\left( {2{x^2} - 3xy + 5{y^2}} \right):3{x^3}{y^2}\\
= 2{x^2} - 3xy + 5{y^2}\\
c)(2{x^3} - 21{x^2} + 67x - 60):(x - 5)\\
= \left( {2{x^3} - 10{x^2} - 11{x^2} + 55x + 12x - 60} \right):\left( {x - 5} \right)\\
= \left[ {2{x^2}\left( {x - 5} \right) - 11x\left( {x - 5} \right) + 12\left( {x - 5} \right)} \right]:\left( {x - 5} \right)\\
= \left( {x - 5} \right)\left( {2{x^2} - 11x + 12} \right):\left( {x - 5} \right)\\
= 2{x^2} - 11x + 12\\
d)({x^4} + 2{x^3} + x - 25):({x^2} + 5)\\
= \left[ {{x^4} + 5{x^2} + 2{x^3} + 10x - 5{x^2} - 25 - 9x} \right]:\left( {{x^2} + 5} \right)\\
= \left[ {{x^2}\left( {{x^2} + 5} \right) + 2x\left( {{x^2} + 5} \right) - 5\left( {{x^2} + 5} \right) - 9x} \right]:\left( {{x^2} + 5} \right)\\
= \left( {{x^2} + 5} \right)\left( {{x^2} + 2x - 5} \right):\left( {{x^2} + 5} \right) - 9x:\left( {{x^2} + 5} \right)\\
= {x^2} + 2x - 5 - \frac{{9x}}{{{x^2} + 5}}\\
e)(27{x^3} - 8):(6x + 9{x^2} + 4)\\
= \left[ {{{\left( {3x} \right)}^3} - {2^3}} \right]:\left( {9{x^2} + 6x + 4} \right)\\
= \left( {3x - 2} \right)\left( {9{x^2} + 6x + 4} \right):\left( {9{x^2} + 6x + 4} \right)\\
= 3x - 2
\end{array}\]

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