To find: Expansion of (2x – 3y)⁴

Formula used: (i)

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

We have, (2x – 3y)⁴

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

⇒ [1(16x⁴)] – [4(8x³)(3y)] + [6(4x²)(9y²)] – [4(2x)(27y³)] + [1(81y⁴)]

⇒ 16x⁴ – 96x³y + 216x²y² – 216xy³ + 81y⁴

Ans) 16x⁴ – 96x³y + 216x²y² – 216xy³ + 81y⁴