The term 𝑥2𝑦2 in the expansion (𝑥 + 2𝑦)5 isa. 10𝑥2𝑦3b. 2𝑥2𝑦3c. Noned. 4𝑥3𝑦2

The term in the expansion of (x + 2y)^5 can be found using the binomial theorem, which states that any term in the expansion can be found using the formula:

(n choose k) * (a^(n-k)) * (b^k)

where:

• n is the power to which the binomial is raised (in this case, 5),
• k is the position of the term in the expansion (starting from 0),
• a is the first term in the binomial (in this case, x), and
• b is the second term in the binomial (in this case, 2y).

We want to find the term x^2y^2. This means we want the power of x to be 2 and the power of y to be 2. Since the power of y is also the number of times we choose the second term in the binomial, k = 2.

Substituting these values into the formula, we get:

(5 choose 2) * (x^(5-2)) * ((2y)^2)

= 10 * x^3 * 4y^2

= 40x^3y^2

So, the term x^2y^2 does not appear in the expansion of (x + 2y)^5. Therefore, the correct answer is c. None.