Final answer:
The binomial theorem is used to expand binomial expressions. The expression (x + y)10 can be expanded using the binomial theorem, resulting in the expression x10 + 10x9y + 45x8y2 + 120x7y3 + 210x6y4 + 252x5y5 + 210x4y6 + 120x3y7 + 45x2y8 + 10xy9 + y10.
Step-by-step explanation:
The binomial theorem states that any binomial expression of the form (a + b)n can be expanded as a sum of terms using the coefficients from Pascal's triangle. In the case of (x + y)10, we can use the binomial theorem to find the expansion.
Using the formula (a + b)n = C(n, 0) * an * b0 + C(n, 1) * an-1 * b1 + C(n, 2) * an-2 * b2 + ... + C(n, n-1) * a1 * bn-1 + C(n, n) * a0 * bn, where C(n, k) represents the binomial coefficient, we can substitute x for a, y for b, and 10 for n.
The expansion of (x + y)10 is: x10 + 10x9y + 45x8y2 + 120x7y3 + 210x6y4 + 252x5y5 + 210x4y6 + 120x3y7 + 45x2y8 + 10xy9 + y10.