To expand the binomial (3x + 2y)^5 using the binomial theorem, we can use the formula:
(3x + 2y)^5 = C(5, 0) * (3x)^5 * (2y)^0 + C(5, 1) * (3x)^4 * (2y)^1 + C(5, 2) * (3x)^3 * (2y)^2 + C(5, 3) * (3x)^2 * (2y)^3 + C(5, 4) * (3x)^1 * (2y)^4 + C(5, 5) * (3x)^0 * (2y)^5
Expanding each term and simplifying, we get:
(3x + 2y)^5 = 1 * (3x)^5 * (2y)^0 + 5 * (3x)^4 * (2y)^1 + 10 * (3x)^3 * (2y)^2 + 10 * (3x)^2 * (2y)^3 + 5 * (3x)^1 * (2y)^4 + 1 * (3x)^0 * (2y)^5
Simplifying further:
(3x + 2y)^5 = 243x^5 + 810x^4y + 1080x^3y^2 + 720x^2y^3 + 240xy^4 + 32y^5
Therefore, the expansion of (3x + 2y)^5 is 243x^5 + 810x^4y + 1080x^3y^2 + 720x^2y^3 + 240xy^4 + 32y^5.