The third term in the expansion of x26 can be calculated by applying the binomial theorem or by recognizing it as part of a polynomial expansion. If we are to consider the expansion of (a + b) to the power of 26, we need to determine the specific nature of the variables ‘a’ and ‘b’. In this case, if we assume that we are expanding (x + 0) for the sake of this explanation, we could say that every term after the first in that straightforward expansion remains x26. However, if we are considering an expansion with multiple elements, we might apply the formula for the binomial expansion:
General term:
Tk = C(n, k) * a(n-k) * bk
Where:
– C(n, k) is the binomial coefficient, that is ‘n choose k’.
– ‘a’ represents the first term of the binomial expression (in this case, ‘x’).
– ‘b’ represents the second term of the binomial expression.
For calculating the third term out of 26, we must take into account k = 2 (since we start from k = 0). For k = 2, our term will be:
T3 = C(26, 2) * x(26-2) * 02 = C(26, 2) * x24 * 0
Since this results in a zero multiplier in our equation, generally leading us to conclude that all terms after the first in a basic expansion as explained would yield results remaining x26.
Therefore, the **answer is: x26**. If different terms were included in the combination for ‘b’, we’d derive different calculations for other polynomial-style expressions.