1. Cho A=xy(x+2y) – x^2.(-7y^2 – x^2) B= y^2.(5x^2 – 2x) – (yx^2 + 3x^4 + 1) Tính 2A-B , A+B 2. Cho P(x) = 2x^3 + x^2 + 5 – 3x + 3x^2 -2x^

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1. Đáp án:

   1)
   $2A-B=3x^2y+6xy^2+9x^2y^2+5x^4+1\\
   A+B=12x^2y^2-2x^4-1\\
   2)
   P(x)=0
   \Leftrightarrow  x=2\\
   P(x)=-|-5|
   \Leftrightarrow x=\dfrac{11}{3}\\$
   3)
   A có  ${\left[\begin{aligned}x=2\\x=3\end{aligned}\right.}$
   B có  $x=\dfrac{-2}{3}$

   Giải thích các bước giải:

    $1)
   A=xy(x+2y) – x^2.(-7y^2 – x^2)\\
   =x^2y+2xy^2+7x^2y^2+x^4\\
    B= y^2.(5x^2 – 2x) – (yx^2 + 3x^4 + 1)\\
   =5x^2y^2-2xy^2-x^2y-3x^4-1\\
   2A-B=2.(x^2y+2xy^2+7x^2y^2+x^4)-(5x^2y^2-2xy^2-x^2y-3x^4-1)\\
   =2x^2y+4xy^2+14x^2y^2+2x^4-5x^2y^2+2xy^2+x^2y+3x^4+1\\
   =(2x^2y+x^2y)+(4xy^2+2xy^2)+(14x^2y^2-5x^2y^2)+(2x^4+3x^4)+1\\
   =3x^2y+6xy^2+9x^2y^2+5x^4+1\\
   A+B=(x^2y+2xy^2+7x^2y^2+x^4)+(5x^2y^2-2xy^2-x^2y-3x^4-1)\\
   =x^2y+2xy^2+7x^2y^2+x^4+5x^2y^2-2xy^2-x^2y-3x^4-1\\
   =(x^2y-x^2y)+(2xy^2-2xy^2)+(7x^2y^2+5x^2y^2)+(x^4-3x^4)-1\\
   =12x^2y^2-2x^4-1\\
   2)
   P(x)=0\\
   \Leftrightarrow  2x^3 + x^2 + 5 – 3x + 3x^2 -2x^3 – 4x^2 + 1=0\\
   \Leftrightarrow (2x^3-2x^3)+(x^2+3x^2-4x^2)-3x+(5+1)=0\\
   \Leftrightarrow -3x=-6\\
   \Leftrightarrow x=2\\
   P(x)=-|-5|=-5\\
   \Leftrightarrow -3x+6=-5\\
   \Leftrightarrow -3x=-11\\
   \Leftrightarrow x=\dfrac{11}{3}\\
   3)
   A=(2-x)+(x-2)^2=0\\
   \Leftrightarrow -(x-2)+(x-2)^2=0\\
   \Leftrightarrow (x-2)(-1+x-2)=0
   \Leftrightarrow (x-2)(x-3)=0\\
   \Leftrightarrow {\left[\begin{aligned}x=2\\x=3\end{aligned}\right.}\\
   B=\dfrac{1}{2}x^3+\dfrac{4}{27}=0\\
   \Leftrightarrow \dfrac{1}{2}x^3=-\dfrac{4}{27}\\
   \Leftrightarrow x^3=\dfrac{-8}{27}\\
   \Leftrightarrow x^3=\left ( \dfrac{-2}{3} \right )^3\\
   \Leftrightarrow x=\dfrac{-2}{3}$

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