x mũ 2-3x mũ 2-4x +12=? 9x mũ hai-36=? x mũ ba -x+3x mũ 2 y+3xy mũ hai+y mũ ba -y ax mũ hai+ay-bx mũ hai-by

Question

x mũ 2-3x mũ 2-4x +12=?
9x mũ hai-36=?
x mũ ba -x+3x mũ 2 y+3xy mũ hai+y mũ ba -y
ax mũ hai+ay-bx mũ hai-by

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Iris 2 tháng 2021-09-27T12:57:43+00:00 1 Answers 12 views 0

Answers ( )

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    2021-09-27T12:59:01+00:00

    \[\begin{array}{l}
    {x^2} – 3{x^2} – 4x + 12 = – 2{x^2} – 4x + 12\\
    = – 2\left( {{x^2} + 2x – 6} \right) = – 2\left[ {\left( {{x^2} + 2x + 1} \right) – 7} \right]\\
    = – 2\left[ {{{\left( {x + 1} \right)}^2} – 7} \right] = – 2\left( {x + 1 – \sqrt 7 } \right)\left( {x + 1 + \sqrt 7 } \right).\\
    9{x^2} – 36 = \left( {3x – 6} \right)\left( {3x + 6} \right).\\
    {x^3} – x + 3{x^2}y + 3x{y^2} + {y^3} – y\\
    = \left( {{x^3} + 3{x^2}y + 3x{y^2} + {y^3}} \right) – \left( {x + y} \right)\\
    = {\left( {x + y} \right)^3} – \left( {x + y} \right)\\
    = \left( {x + y} \right)\left[ {{{\left( {x + y} \right)}^2} – 1} \right]\\
    = \left( {x + y} \right)\left( {x + y – 1} \right)\left( {x + y + 1} \right)\\
    a{x^2} + ay – b{x^2} – by\\
    = {x^2}\left( {a – b} \right) + y\left( {a – b} \right)\\
    = \left( {a – b} \right)\left( {{x^2} + y} \right).
    \end{array}\]

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