a4 - 1 = ( a2 )2 - ( 1 )2= ( a2 + 1 )( a2 - 1 ) [ ∵ a2 - b2 = ( a + b )( a - b )]= ( a2 + 1 )[ (a)2 - (1)2 ]= ( a2 + 1 )( a + 1 )( a - 1 )

Factorise : A4 - 1 | Shaalaa.com

Factorise : a⁴ - 1

Sum

a⁴ - 1
= ( a² )² - ( 1 )²
= ( a² + 1 )( a² - 1 ) [ ∵ a² - b² = ( a + b )( a - b )]
= ( a² + 1 )[ (a)² - (1)²]
= ( a² + 1 )( a + 1 )( a - 1 )

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Method of Factorisation : Difference of Two Squares

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Chapter 5: Factorisation - Exercise 5 (C) [Page 72]

Chapter 5 Factorisation
Exercise 5 (C) | Q 9 | Page 72

Factorise : A4 - 1