Question

Without expanding, find the value of

(x + 1)⁴ – 4(x + 1)³ (x – 1) + 6(x + 1)² (x – 1)² – 4(x + 1) (x – 1)³ + (x – 1)⁴

Answer 1

Let x + 1 = a and x - 1 = b

We notice that 1, 4, 6, 1 are the values of ⁴C₀, ⁴C₁, ⁴C₂, ⁴C₃, ⁴C₄ respectively.

\(\therefore\) The given expression becomes