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Coefficient of a power of x in a product of expansions

This type of question, asked 7 times: 2021 Paper 11, 28 Jun 2022, 27 Jan 2024, 31 Jan 2024, 1 Feb 2024, 5 Apr 2024, 21 Jan 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 11

    52
    The coefficient of x256x^{256} in the expansion of (1−x)101(x2+x+1)100(1 - x)^{101}\left( x^{2}+ x + 1 \right)^{100} is:

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  2. Question 2

    28 Jun 2022

    154
    The term independent of xx in the expression of (1−x2+3x3)(52x3−15x2)11,x≠0\left( 1 -x^{2}+ 3x^{3} \right)\left( \frac{5}{2}x^{3}-\frac{1}{5x^{2}} \right)^{11},x \neq 0 is

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  3. Question 3

    27 Jan 2024

    175
    The coefficient of x2012x^{2012} in the expansion of (1−x)2008(1+x+x2)2007(1 - x)^{2008}\left( 1 + x +x^{2} \right)^{2007} is equal to

  4. Question 4

    31 Jan 2024

    85
    In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5,x≠0(1 +x)\left( 1 -x^{2} \right)\left( 1 +\frac{3}{x}+\frac{3}{x^{2}}+\frac{1}{x^{3}} \right)^{5},x\neq 0, the sum of the coefficient of x3x^{3} and x−13x^{- 13} is equal to

  5. Question 5

    1 Feb 2024

    83
    If the Coefficient of x30x^{30} in the expansion of (1+1x)6(1+x2)7(1−x3)8;x≠0\left( 1 +\frac{1}{x} \right)^{6}\left( 1 +x^{2} \right)^{7}\left( 1 -x^{3} \right)^{8};x \neq 0 is α\alpha, then ∣α∣|\alpha| equals

  6. Question 6

    5 Apr 2024

    82
    If the constant term in the expansion of (1+2x−3x3)(32x2−13x)9\left( 1 + 2x- 3x^{3} \right)\left( \frac{3}{2}x^{2}-\frac{1}{3x} \right)^{9} is pp, then 108p108p is equal to

  7. Question 7

    21 Jan 2026 S1

    66
    If the coefficient of xx in the expansion of (ax2+bx+c)(1−2x)26\left( ax^{2}+ bx + c \right)(1 - 2x)^{26} is -56 and the coefficients of x2x^{2} and x3x^{3} are both zero, then a+b+ca + b + c is equal to

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