Bài 1: Rút gọn: c) (a^2 – 1)^3 – ( a^4 + a^2 + 1)(a^2 – 1) d) ( a^4 – 3a^2 + 9)( a^2 + 3) – ( 3 + a^2)^3 Bài 2: Tìm x: b) (x – 2)^3 – (x – 3)(x^2 + 3x

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1. Đáp án:

    $1)
   c) 3a^4+3a^2\\
   d) -54-27a^2-9a^4\\
   2)
   b)  x=1\\
   3)
   -30$
   Giải thích các bước giải:

    $1)
   c) (a^2 – 1)^3 – ( a^4 + a^2 + 1)(a^2 – 1)\\
   =(a^2)^3-3a^4+3a^2-1-\left [(a^2)^3-1^3  \right ]\\
   =a^6-3a^4+3a^2-1-a^6+1\\
   =3a^4+3a^2\\
   d) ( a^4 – 3a^2 + 9)( a^2 + 3) – ( 3 + a^2)^3\\
   =(a^2)^3-3^3-(27+27a^2+9a^4+a^6)\\
   =a^6-27-27-27a^2-9a^4-a^6\\
   =-54-27a^2-9a^4\\
   2)
   b) (x – 2)^3 – (x – 3)(x^2 + 3x + 9) + 6(x + 1)^2 = 49\\
   \Leftrightarrow x^3-6x^2+12x-8-(x^3-3^3)+6(x^2+2x+1)-49=0\\
   \Leftrightarrow x^3-6x^2+12x-8-x^3+27+6x^2+12x+6-49=0\\
   \Leftrightarrow 24x-24=0\\
   \Leftrightarrow 24x=24\\
   \Leftrightarrow x=1\\
   3)
   (x – 1)^3 – 4x(x + 1)(x – 1) + 3(x – 1)(x^2 + x + 1)\\
   =x^3-3x^2+3x-1-4x(x^2-1)+3(x^3-1)\\
   =x^3-3x^2+3x-1-4x^3+4x+3x^3-3\\
   =-3x^2+7x-4$
   Thay $x=-2$ ta được 
   $-3.(-2)^2+7.(-2)-4=(-3).4-14-4=-30$
   4)
   $(x – 1)^3 – (x – 1)(x^2 + x + 1) + 3(x – 1)x\\
   =x^3-3x^2+3x-1-(x^3-1)+3x^2-3x\\
   =x^3-3x^2+3x-1-x^3+1+3x^2-3x\\
   =(x^3-x^3)+(-3x^2+3x^2)+(3x-3x)+(-1+1)
   =0$

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