The value of (a + 1) (a - 1) (a² + 1) is a⁴ - 1. Is the given statement true or false

Solution:

The statement, ‘The value of (a + 1) (a - 1) (a² + 1) is a⁴ - 1’ is true.

Given, (a + 1) (a - 1) (a² + 1)

Using standard identity: (a + b) (a - b) = a² - b²

⇒ (a² - 1²) (a² + 1²)

= (a²)² - (1²)²

= a⁴ - 1

✦ Try This: State true or false: the value of (x + 3) (x - 3) (x² - 9) = x⁴ - 81

The statement the value of (x + 3) (x - 3) (x² - 9) = x⁴ - 81 is false

Given, (x + 3) (x - 3) (x² - 9)

Using standard identity: (a + b) (a - b) = a² - b²

⇒ (x² - 3²)(x² - 9)

⇒(x² - 9)(x² - 9)

⇒(x² - 9)²

Using the identity (a - b)² = a² - 2ab + b²

⇒(x² - 9)² = (x²)² - 2(x²)(9) + (9)²

= x⁴ - 18x² + 81

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 80

The value of (a + 1) (a - 1) (a² + 1) is a⁴ - 1. Is the given statement true or false

Summary:

The statement, ‘The value of (a + 1) (a - 1) (a² + 1) is a⁴ - 1’ is true

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