Find the number of terms in the expansion of: from Mathematics
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    Binomial Theorem
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    Find the number of terms in the expansion of:
    left parenthesis straight x minus 2 straight y right parenthesis to the power of straight m comma space straight m space element of space straight N
    left parenthesis straight x minus 2 straight y right parenthesis to the power of straight m comma space straight m space element of space straight N space rightwards double arrow space straight n space equals space straight m

    ∴ Number of terms in the expansion = n + 1 = m + 1          (∵ n = m)
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    Find the number of terms in the expansion of:
    open parentheses straight x over 2 minus 3 over straight x close parentheses to the power of 11
    open parentheses straight x over 2 minus 3 over straight x close parentheses to the power of 11 space rightwards double arrow space space straight n space equals space 11

    ∴  Number of terms in the expansion = n + 1 = 11 + 1 = 12
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    Find the number of terms in the expansion of:
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    left parenthesis 1 plus 2 straight x plus straight x squared right parenthesis to the power of 4 space equals space left square bracket left parenthesis 1 plus straight x right parenthesis squared right square bracket to the power of 4 space equals space left parenthesis 1 plus straight x right parenthesis to the power of 8 space rightwards double arrow space straight n space equals space 8

    ∴ Number of terms in the expansion = n + 1 = 8 + 1 = 9
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    Find the number of terms in the expansion of:
    left parenthesis 2 minus 3 straight x right parenthesis to the power of 6

    left parenthesis 2 minus 3 straight x right parenthesis to the power of 6
                    n = 6

    ∴    Number of terms in expansion = n + 1 = 6 + 1 = 7
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    Find the number of terms in the expansion of:
    left parenthesis 1 plus straight x plus straight x squared right parenthesis cubed
    left parenthesis 1 plus straight x plus straight x squared right parenthesis cubed
    left parenthesis 1 plus straight x plus straight x squared right parenthesis is not reducible to the binomial form a + b; n = 3.
    rightwards double arrow Number of terms  in the expansion = fraction numerator left parenthesis straight n plus 1 right parenthesis space left parenthesis straight n plus 2 right parenthesis over denominator 2 end fraction space equals space fraction numerator left parenthesis 3 plus 1 right parenthesis left parenthesis 3 plus 2 right parenthesis over denominator 2 end fraction equals fraction numerator 4 cross times 5 over denominator 2 end fraction equals 10
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