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Find the coefficient of fourth term of (-x -3)^5

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Final answer:

The coefficient of the fourth term of (-x -3)^5 is -270x^2.

Step-by-step explanation:

To find the coefficient of the fourth term of (-x -3)^5, we need to determine the pattern of the terms in the expansion.

The general formula for the binomial expansion of (a + b)^n is (n choose k) * a^(n-k) * b^k, where (n choose k) represents the binomial coefficient. In this case, a is -x and b is -3.

So, the fourth term is obtained when k = 3:

(5 choose 3) * (-x)^(5-3) * (-3)^3 = 10 * x^2 * -27 = -270x^2.

User Amin Kiany
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