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Find the coefficient of x^4 in the expan...

Find the coefficient of `x^4` in the expansion of `(1+x+x^2+x^3)^(6)dot`

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To find the coefficient of \( x^4 \) in the expansion of \( (1 + x + x^2 + x^3)^6 \), we can follow these steps: ### Step 1: Rewrite the expression We can rewrite \( (1 + x + x^2 + x^3)^6 \) as \( (1 + x + x^2 + x^3)^6 \). ### Step 2: Use the multinomial theorem The multinomial theorem states that: \[ ...
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Knowledge Check

  • Find the coefficient of x^(11) in the expansion of (1+2x+x^(2))^(6)

    A
    1
    B
    2
    C
    6
    D
    12

  • The coefficient of x^(4) in the expansion of (1+x+x^(2))^(6) is

    A
    72
    B
    90
    C
    96
    D
    112

  • Find the coefficient of x^6 y^3 in the expansion of (x+2y) .

    A
    972
    B
    `""^(9) C_3 2^3`
    C
    `""^(9) C_3`
    D
    `152`

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    Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11) .

    Find the coefficient of x^4 in the expansion of (1 – 9x + 20x^2)^(-1) .

    Find the coefficient of x^4 in the expansion of (1+x+x^2 +x^3 )^11 x^4 in the expansion of (2-x+ 3 x^2)^6

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