a)x^4+2x^3-2x^2-1 b)x^2+2x-4y^2-4y c)a^2(b-c)+b^2(c-a)+c^2(a-b) d)(x-y)^3+(x-z)^3+(z-x)^3

Bởi

a)x^4+2x^3-2x^2-1
b)x^2+2x-4y^2-4y
c)a^2(b-c)+b^2(c-a)+c^2(a-b)
d)(x-y)^3+(x-z)^3+(z-x)^3

0 bình luận về “a)x^4+2x^3-2x^2-1 b)x^2+2x-4y^2-4y c)a^2(b-c)+b^2(c-a)+c^2(a-b) d)(x-y)^3+(x-z)^3+(z-x)^3”

  1. a)x^4+2x³-2x²-1

    =(x²)²-1+2x³-2x²

    =(x²-1)(x²+1)+2x³-2x²

     =(x-1)(x+1)(x²+1)+2x²(x-1)

    =(x-1)[(x+1)(x²+1)+2x²]

    =(x-1)[x³+x+x²+1+2x²]

    =(x-1)[x³+3x²+x+1]

    =(x-1)(x³+3x²+x+1)

    b)x²+2x-4y²-4y

    =x²+2x+1-(2y)²-2.y.2-1

    =(x²+2x+1)-[(2y)²+2.y.2+1]

    =(x+1)²-(2y+1)²

    =[(x+1)-(2y+1)][(x+1)+(2y+1)]

    =(x+1-2y-1)(x+1+2y+1)

    =(x-2y)(x+2y+2)

    c)a²(b-c)+b²(c-a)+c²(a-b)

    =a²b-a²c+b²c-ab²+ac²-bc²

    =a²b-ab²-a²c+b²c+ac²-bc²

    =ab(a-b)-c(a²-b²)+c²(a-b)

    =ab(a-b)-c(a-b)(a+b)+c²(a-b)

    =(a-b)[ab-c(a+b)+c²]

    =(a-b)(ab-ac-bc+c²)

    =(a-b)(ab-bc-ac+c²)

    =(a-b)[b(a-c)-c(a-c)]

    =(a-b)[(a-c)(b-c)]

    =(a-b)(a-c)(b-c)

    d)(x-y)³+(x-z)³+(z-x)³

    =x³-3x²y+3xy²-y³+{(x-z+z-x)[(x-z)²-(x-z)(z-x)+(z-x)²}

    =x³-3x²y+3xy²-y³+(0.[(x-z)²-(x-z)(z-x)+(z-x)²]

    =x³-3x²y+3xy²-y³+0

    =x³-3x²y+3xy²-y³

    Chúc bạn học tốt!!!             ^_^  ^_^  ^_^

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