Find the 2 nd term in the expansion of (3x-4y)^(4) in simplest form. Answer:

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Find the 2 nd term in the expansion of  (3x-4y)^(4) in simplest form. Answer:

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Apply Binomial Theorem: To find the second term in the expansion of (3x-4y)^(4), we will use the binomial theorem. The binomial theorem states that (a+b)^n expands to a series of terms that involve powers of a and b, with coefficients determined by the binomial coefficients. The general term in the expansion is given by the formula: T(k+1) = nCk * a^(n-k) * b^k, where nCk is the binomial coefficient, a and b are the terms in the binomial, n is the power, and k is the term number minus one.Calculate Binomial Coefficient: We are looking for the second term, which means k=1. The binomial coefficient for the second term when n=4 and k=1 is 4C1, which is equal to 4. This is because 4C1 = 4! / (1! * (4-1)!) = 4 / 1 = 4.Use Formula for Second Term: Now we will plug in the values into the formula for the second term: T(2) = 4C1 * (3x)^(4-1) * (-4y)^1. This simplifies to T(2) = 4 * (3x)^3 * (-4y).Calculate (3x)^3 and (-4y): Next, we calculate (3x)^3 and (-4y). (3x)^3 = 3^3 * x^3 = 27x^3, and (-4y) is simply -4y.Multiply Terms to Find Second Term: Multiplying these together with the binomial coefficient we found earlier, we get T(2) = 4 * 27x^3 * (-4y) = 4 * -108x^3 * y = -432x^3y.

Find the $2$ nd term in the expansion of $(3 x-4 y)^{4}$ in simplest form. $\newline$ Answer:

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Find the $2$ nd term in the expansion of $(3 x-4 y)^{4}$ in simplest form. $\newline$ Answer: