phân tích a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3) thành nhân tử

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phân tích a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3) thành nhân tử

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Katherine 1 năm 2021-10-04T02:09:00+00:00 1 Answers 2 views 0

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    2021-10-04T02:10:23+00:00

    Đáp án:

     `\qquad a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)`

    `=(a-b)(b-c)(c-a)(a+b+c)`

    Giải thích các bước giải:

    `\qquad a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)`

    `=a(b^3-c^3)+b(c^3-a^3)-c(c^3-a^3+b^3-c^3)`

    `=[a(b^3-c^3)-c(b^3-c^3)]+[b(c^3-a^3)-c(c^3-a^3)]`

    `=(b^3-c^3)(a-c)+(c^3-a^3)(b-c)`

    `=(b-c)(b^2+bc+c^2)(a-c)+(c-a)(c^2+ac+a^2)(b-c)`

    `=(b-c)(a-c)(b^2+bc+c^2-c^2-ac-a^2)`

    `=(b-c)(a-c)(b^2-a^2+bc-ac)`

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

    `=(b-c)(a-c)(b-a)(b+a+c)`

    `=(a-b)(b-c)(c-a)(a+b+c)`

    $\\$

    Vậy `a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)`

    `=(a-b)(b-c)(c-a)(a+b+c)`

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