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    I'm doing my A levels and really stuck on this question. I came across it on a past paper.

    The expansion of (1-x)(a+bx)^3 in ascending powers of x begins 8 - 28x....
    Find the values of a and b.

    I have already expanded (a+bx)^3 to give a³ + 3a²bx + 3ab²x² + b³x³

    How do I do the second part - finding a and b?

    OK - you've done the first bit.

    Now you can multiply what you've got by the (1-x) so you get the series for the whole thing.

    Then you look at the coefficients. How many units have you got? a^3. How many are you told that you have? 8. So you have a.

    Then you look at how many x's you have. You have a already. So figure out b.
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