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now, how do we get the coefficients? well, the first coefficient is 1, any subsequent is " the product of the current terms's coefficient and the exponent of the first element, divided by the exponent of the second element in the next term", now that's a mouthful, but for example,
how did get 210 for the 5th expanded term? well is just 120 * 7 / 4
how about 252 of the 6th term? 210 * 6 / 5.
how about 45 of the 9th one? 120 * 3 / 8.
of course, the exponents for each is simple, as you'd already know from the binomial theorem.
so, just expand away the 9th expanded term.