Phân tích thành nhân tử: a, ( ab – 1 )2 + ( a+b )2 c,x3 – 4×2 +12 x – 27 b, x3 +2×2 +2x + 1 d, x4 – 2×3 +2x +1 e,x4 +2×3 + 2×2 +2x +1

Phân tích thành nhân tử:
a, ( ab – 1 )2 + ( a+b )2
c,x3 – 4×2 +12 x – 27
b, x3 +2×2 +2x + 1
d, x4 – 2×3 +2x +1
e,x4 +2×3 + 2×2 +2x +1

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  1. Đáp án:

    $\begin{array}{l}
    a){\left( {ab – 1} \right)^2} + {\left( {a + b} \right)^2}\\
     = {a^2}{b^2} – 2ab + 1 + {a^2} + 2ab + {b^2}\\
     = {a^2}{b^2} + 1 + {a^2} + {b^2}\\
     = {a^2}\left( {{b^2} + 1} \right) + \left( {{b^2} + 1} \right)\\
     = \left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)\\
    c){x^3} – 4{x^2} + 12x – 27\\
     = {x^3} – 27 + \left( { – 4{x^2} + 12x} \right)\\
     = \left( {x – 3} \right)\left( {{x^2} + 3x + 9} \right) – 4x\left( {x – 3} \right)\\
     = \left( {x – 3} \right)\left( {{x^2} + 3x + 9 – 4x} \right)\\
     = \left( {x – 3} \right)\left( {{x^2} – x + 9} \right)\\
    b){x^3} + 2{x^2} + 2x + 1\\
     = {x^3} + 2{x^2} + x + x + 1\\
     = x\left( {{x^2} + 2x + 1} \right) + \left( {x + 1} \right)\\
     = x{\left( {x + 1} \right)^2} + \left( {x + 1} \right)\\
     = \left( {x + 1} \right)\left( {x\left( {x + 1} \right) + 1} \right)\\
     = \left( {x + 1} \right)\left( {{x^2} + x + 1} \right)\\
    d){x^4} – 2{x^3} + 2x – 1\\
     = {x^4} – 2{x^3} + {x^2} – {x^2} + 2x – 1\\
     = {x^2}\left( {{x^2} – 2x + 1} \right) – \left( {{x^2} – 2x + 1} \right)\\
     = \left( {{x^2} – 2x + 1} \right)\left( {{x^2} – 1} \right)\\
     = {\left( {x – 1} \right)^2}\left( {x – 1} \right)\left( {x + 1} \right)\\
     = {\left( {x – 1} \right)^3}\left( {x + 1} \right)\\
    e){x^4} + 2{x^3} + 2{x^2} + 2x + 1\\
     = {x^4} + 2{x^3} + {x^2} + {x^2} + 2x + 1\\
     = {x^2}\left( {{x^2} + 2x + 1} \right) + \left( {{x^2} + 2x + 1} \right)\\
     = \left( {{x^2} + 2x + 1} \right)\left( {{x^2} + 1} \right)\\
     = {\left( {x + 1} \right)^2}\left( {{x^2} + 1} \right)
    \end{array}$

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  2. Đáp án:

    a)(ab1)2+(a+b)2

    =a2b22ab+1+a2+2ab+b2

    =a2b2+1+a2+b2=a2(b2+1)+(b2+1(a2+1)(b2+1)

    c)x34x2+12x27

    =x327+(4x2+12x)

    =(x3)(x2+3x+9)4x(x3)

    =(x3)(x2+3x+94x)

    =(x3)(x2x+9)

    b)x3+2x2+2x+1

    =x3+2x2+x+x+1

    =x(x2+2x+1)+(x+1)

    =x(x+1)2+(x+1)

    =(x+1)(x(x+1)+1)

    =(x+1)(x2+x+1)

    d)x42x3+2x1

    =x42x3+x2x2+2x1

    =x2(x22x+1)(x22x+1)

    =(x22x+1)(x21)

    =(x1)2(x1)(x+1)

    =(x1)3(x+1)

    e)x4+2x3+2x2+2x+1

    =x4+2x3+x2+x2+2x+1

    =x2(x2+2x+1)+(x2+2x+1)

    =(x2+2x+1)(x2+1)

    =(x+1)2(x2+1)

     

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