State whether the statements are true (T) or false (F).

The value of (a+1) (a-1) (a²+1) is a⁴-1

Solving it, we get

(a + 1)(a – 1)(a² + 1) = {(a + 1)(a – 1)} × (a² + 1)

⇒ (a + 1)(a – 1)(a² + 1) = (a² – 1)(a² + 1)

[∵, (x + y)(x – y) = x² – y²; Put x = a and y = 1 ⇒ (a + 1)(a – 1) = a² – 1]

⇒ (a + 1)(a – 1)(a² + 1) = a⁴ – 1

[∵, (x² + y²)(x² – y²) = x⁴ – y⁴; Put x = a and y = 1 ⇒ (a² + 1)(a² – 1) = a⁴ – 1]

Thus, the value of (a + 1)(a – 1)(a² + 1) is a⁴ – 1.

Hence, the statement is true.