To find: Expansion of (3x + 2y)⁵

Formula used: (i)

(ii) (a+b)ⁿ =   ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + …… +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ

We have, (3x + 2y)⁵

⇒  [⁵C₀(3x)^5-0] + [⁵C₁(3x)^5-1(2y)¹] + [⁵C₂(3x)^5-2(2y)²] + [⁵C₃(3x)^5-3(2y)³]+ [⁵C₄(3x)^5-4(2y)⁴] + [⁵C₅(2y)⁵]

⇒ [1(243x⁵)] + [5(81x⁴)(2y)] + [10(27x³)(4y²)] + [10(9x²)(8y³)] + [5(3x)(16y⁴)] + [1(32y⁵)]

⇒ 243x⁵ + 810x⁴y + 1080x³y² + 720x²y³ + 240xy⁴ + 32y⁵

Ans) 243x⁵ + 810x⁴y + 1080x³y² + 720x²y³ + 240xy⁴ + 32y⁵