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

Answer:

16

Step-by-step explanation:

Hi,

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

then (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

  will become a⁴ + ⁴C₁a³b + ⁴C₂a²b² + ⁴C₃ab³ + ⁴C₄b⁴

But the above is the expansion of (a + b)⁴

Thus, the given expression is equal to (a + b)⁴

= (2x - 1 + 3 - 2x)⁴

= 2⁴

= 16

Hence the value of the given expression is 16.

Hope, it helps !