1,16x^3+54y^3 2,x^2-2xy+y^2-16 3,x^3+x^2-x+2 4,2x^2-2y^2-6x-6y 5,x^4-5x^2+4

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1. Đáp án:

    Bạn tham khảo nhé!!!

   Giải thích các bước giải:

   $\begin{array}{l}
   1)\,\,\,16{x^3} + 54{y^3} = 2\left( {8{x^3} + 27{y^3}} \right)\\
    = 2\left( {2x + 3y} \right)\left( {4{x^2} – 6xy + 9{y^2}} \right).\\
   2)\,\,{x^2} – 2xy + {y^2} – 16 = {\left( {x – y} \right)^2} – 16\\
    = \left( {x – y – 4} \right)\left( {x – y + 4} \right).\\
   3)\,\,{x^3} + {x^2} – x + 2 = {x^3} + 2{x^2} – {x^2} – 2x + x + 2\\
    = {x^2}\left( {x + 2} \right) – x\left( {x + 2} \right) + \left( {x + 2} \right)\\
    = \left( {x + 2} \right)\left( {{x^2} – x + 1} \right).\\
   4)\,\,2{x^2} – 2{y^2} – 6x – 6y = 2\left( {{x^2} – {y^2}} \right) – 6\left( {x + y} \right)\\
    = 2\left( {x – y} \right)\left( {x + y} \right) – 6\left( {x + y} \right)\\
    = 2\left( {x + y} \right)\left( {x – y – 3} \right).\\
   5)\,\,\,{x^4} – 5{x^2} + 4 = {x^4} – {x^2} – 4{x^2} + 4\\
    = {x^2}\left( {{x^2} – 1} \right) – 4\left( {{x^2} – 1} \right)\\
    = \left( {{x^2} – 1} \right)\left( {{x^2} – 4} \right)\\
    = \left( {x – 1} \right)\left( {x + 1} \right)\left( {x – 2} \right)\left( {x + 2} \right).
   \end{array}$

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