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Find the first three terms in the expansion of (14 - 3x)^n in descending power. a) 196x^3 - 588x^2 + 588x - 196 b) 196x^3 - 588x^2 + 588x + 196 c) 196x^3 + 588x^2 + 588x - 196 d) 196x^3 + 588x^2 - 588x + 196

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The expansion of a polynomial is done using the binomial theorem, which states that for any numbers a and b, the equation (a - b)^n is equal to the sum from k=0 to n of [n choose k] * a^(n-k) * (b^k).

In this problem, a = 14 and b = 3x.

To find the first three terms of the expansion of (14 - 3x)^n we need to substitute n, a, b into the binomial theorem equation for k = 0, k = 1, and k = 2.

When k = 0, we have:
[n choose 0] * 14^n * (3x)^0 = 14^n

When k = 1, we have:
[n choose 1] * 14^(n-1) * (3x)^1 = n*14^(n-1) * 3x

When k = 2, we have:
[n choose 2] * 14^(n-2) * (3x)^2 = [n*(n-1)/2] * 14^(n-2) * 9x^2

Note that for any positive integer n, [n choose 0] equals to 1 and [n choose 1] equals to n. Be further aware that "(3x)^1" is just 3x, and "(3x)^2" is 9x^2.

We are looking for the first three terms in the expansion of (14 - 3x)^n in descending power. Therefore, the first term is 14^n, the second term is - 3n * 14^(n-1) * x and the third term is 4.5n(n-1) * 14^(n-2) * x^2.

Taking into consideration the options we have been given, it's clear none of them represent the expressions we have found. As such, it seems there may be a mistake in the given options.

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