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

Answer:

16

Step-by-step explanation:

Hi,

Let a = x + 1

b = x - 1

Given expression (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 would 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  

= (x + 1 - (x - 1))⁴

=  2⁴

= 16

Hence, the value of the given expression is 16.

Hope, it helps !