Expand and simplify

Question

(2x^2-3y)^4

Answer 1

(2x² - 3y)⁴

From the binomial theorem,

(2x² + (- 3y))⁴ = 4c₀(2x²)⁴(- 3y)⁰ + 4c₁(2x²)^{4 - 1}(- 3y)¹ + 4c₂(2x²)^{4 - 2}(- 3y)² + 4c₃(2x²)^{4 - 3}(- 3y)³ + 4c₄(2x²)^{4 - 4}(- 3y)⁴

(2x² - 3y)⁴ = 4c₀(16x⁸)(1) - 4c₁(8x⁶)(3y) + 4c₂(4x⁴)(9y²) - 4c₃(2x²)(27y³) + 4c₄(81y⁴)

Substitute the values 4c₀ = 1, 4c₁= 4,  4c₂ = 6, 4c₃ = 4, and 4c₄ = 1.

(2x² - 3y)⁴ = 1(16x⁸) - 4(8x⁶)(3y) + 6(4x⁴)(9y²) - 4(2x²)(27y³) + 1(81y⁴)

(2x² - 3y)⁴ = 16x⁸ - 96x⁶y + 216x⁴y² - 216x²y³ + 81y⁴.