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17 January, 23:29

Find K in the expansion (m-2n) ^10.

M^10 - 20m^9 n + km^8 n^2 - ... + 1024 n^10

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  1. 17 January, 23:33
    0
    10 10 10 10

    (m-2n) ¹⁰ = (0) m¹⁰n⁰ - (1) m¹⁰ (2n) ¹ + (2) m⁸ (2n) ² + ... + (10) m° (2n) ¹⁰

    10

    km⁸n² = (2) m⁸ (2n) ²

    10

    (2) = 10! / (10-2) !2!=10.9.8! / (8!.2!) = 45

    (2n) ²=4n²

    Then:

    Km⁸n²=45m⁸ (4n²)

    Km⁸n²=180m⁸n²

    K=180

    answer: K=180
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