Prove that ∑ᵣ₌₀ⁿ 3ʳ ⁿCᵣ = 4ⁿ.

Binomial Coefficients

Find (a + b)⁴ – (a – b)⁴. Hence, evaluate (√3 +√2)⁴ – (√3 – √2)⁴.

TextBinomial Coefficients

Find (x + 1)⁶ + (x – 1)⁶. Hence or otherwise evaluate (√2 + 1)⁶ + (√2 – 1)⁶.

TextBinomial Coefficients

Find the value of (a² + √(a²–1))⁴ + (a² – √(a²–1))⁴.