Question

Without expanding, find the value of

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

Answer 1

Let 2x - 1 = a and 3 - 2x = b

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

\(\therefore\) The given expression becomes