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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: 11/ x^3 – x^2 – 3x + 27 12/ x^3 + 2x^2 – 2x – 1 16* / 4x(x + 1)^2 – 5x^2 (x + 1) – 4(x+1)

Toán Lớp 8: 11/ x^3 – x^2 – 3x + 27
12/ x^3 + 2x^2 – 2x – 1
16* / 4x(x + 1)^2 – 5x^2 (x + 1) – 4(x+1)

Comments ( 2 )

  1. Giải đáp:
     
    Lời giải và giải thích chi tiết:
     11, x^3 – x^2 – 3x + 27
    = (x^3 + 27) – (x^2 + 3x)
    = (x^3 + 3^3) – x(x + 3)
    = (x + 3)(x^2 – 3x + 9) – x(x + 3)
    = (x + 3)(x^2 – 3x + 9 – x)
    = (x + 3)(x^2 – 4x + 9)
    12, x^3 + 2x^2 – 2x – 1
    = (x^3 – 1) + (2x^2 – 2x)
    = (x – 1)(x^2 + x + 1) + 2x(x – 1)
    = (x – 1)(x^2 + x + 1 + 2x)
    = (x – 1)(x^2 + 3x + 1)
    16, 4x(x + 1)^2 – 5x^2 (x + 1) – 4(x + 1)
    = (x + 1)[4x(x + 1) – 5x^2 – 4]
    = (x + 1)(4x^2 + 4x – 5x^2 – 4)
    = (x + 1)(-x^2 + 4x – 4)
    = (x + 1)[-(x^2 – 4x + 4)]
    = -(x + 1)(x^2 – 2.x.2 + 2^2)
    = -(x + 1)(x – 2)^2

  2. Giải đáp:
    $\displaystyle \begin{array}{{>{\displaystyle}l}} 11.\ ( x+3)\left( x^{2} -4x+9\right)\\ 12.\ ( x-1)\left( x^{2} +3x+1\right)\\ 13.\ -( x+1)( x-2)^{2} \end{array}$
    Lời giải và giải thích chi tiết:
    $\displaystyle \begin{array}{{>{\displaystyle}l}} 11.\ x^{3} -x^{2} -3x+27\\ =x^{3} +3x^{2} -4x^{2} -12x+9x+27\\ =x^{2}( x+3) -4x( x+3) +9( x+3)\\ =( x+3)\left( x^{2} -4x+9\right)\\ 12.\ x^{3} +2x^{2} -2x-1\\ =x^{3} -x^{2} +3x^{2} -3x+x-1\\ =x^{2}( x-1) +3x( x-1) +( x-1)\\ =( x-1)\left( x^{2} +3x+1\right)\\ 13.\ 4x( x+1)^{2} -5x^{2}( x+1) -4( x+1)\\ =( x+1)\left( 4x( x+1) -5x^{2} -4\right)\\ =( x+1)\left( 4x^{2} +4x-5x^{2} -4\right)\\ =( x+1)\left( -x^{2} +4x-4\right)\\ =-( x+1)( x-2)^{2} \end{array}$

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222-9+11+12:2*14+14 = ? ( )

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