The term 𝑥2𝑦2 in the expansion (𝑥 + 2𝑦)5 is

To find the term x^2y^2 in the expansion of (x + 2y)^5, we can use the binomial theorem, which states that:

(a + b)^n = Σ (n choose k) * a^(n-k) * b^k

where "n choose k" is a binomial coefficient, and the sum is from k=0 to n.

In this case, a = x, b = 2y, and n = 5. We want to find the term where the power of x is 2 and the power of y is 2. This corresponds to k = 3 (because a^(n-k) = x^(5-3) = x^2 and (2y)^k = (2y)^3 = 8y^3 = 2^2 * y^2).

So, the term x^2y^2 in the expansion of (x + 2y)^5 is:

(5 choose 3) * x^2 * (2y)^3 = 10 * x^2 * 8y^3 = 80x^2y^3

So, the term x^2y^2 does not appear in the expansion of (x + 2y)^5. The closest term is 80x^2y^3.