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C2 MAT Question Help {Binomial Expansion} watch

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    So the first one is a question and the second one is the answer for the question.

    I can understand powers of a & b add up to make 8 but I'm unsure how they just ignored the 1 in the brackets and how they got 2k in the equation.

    Please Help.
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    (Original post by Denisi007)

    So the first one is a question and the second one is the answer for the question.

    I can understand powers of a & b add up to make 8 but I'm unsure how they just ignored the 1 in the brackets and how they got 2k in the equation.

    Please Help.
    They've not ignored the 1 in the bracket. If we add some brackets, you can see that they are taking the binomial expansion of:

    (1+[xy+y^2])^n

    That is a=1,b=xy+y^2 in the standard binomial expansion.

    Terms in that expansion will be \displaystyle\binom{n}{k}(xy+y^2  )^k

    Now, each term in the brackets has a sum of powers of 2.

    xy: x=1,y=1, total=2
    y^2:x=0,y=2, total =2

    And when you raise what's in the brackets to the power of k, the power of any terms in the result will be 2k.
 
 
 
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