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Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
The general term of a binomial expansion can be set using the following formula:
C(n, k) * x^k * y^(n-k)
where n is the degree of the binomial, C(n, k) is the binomial coefficient, k is the exponent of x, n-k is the exponent of y, and x and y are the terms being expanded.
The binomial coefficient C(n, k) represents the number of ways to choose k items from a set of n items. It can be calculated using the following formula:
C(n, k) = n! / (k! * (n-k)!)
where n! is the factorial of n, and k! and (n-k)! are the factorials of k and n-k, respectively.
For example, consider the expansion of (x + y)^3. The general term of this expansion can be set as follows:
C(3, k) * x^k * y^(3-k)
where k can take on 0, 1, 2, and 3 corresponding to the terms x^3, x^2y, xy^2, and y^3 in the expansion. The binomial coefficient C(3, k) can be calculated using the formula above for each value of k.
