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Question

(2x + 1)^4?

Answer 1

(2x + 1)⁴

From the binomial theorem,

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

(2x + 1)⁴ = 4c₀(16x⁴) + 4c₁(8x³) + 4c₂(4x²) + 4c₃(2x) + 4c₄

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

(2x + 1)⁴ = 1(16x⁴) + 4(8x³) + 6(4x²) + 4(2x) + 1

(2x + 1)⁴ = 16x⁴ + 32x³ + 24x² + 8x + 1.