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Factorisation — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSFactorisation2 Marks
Question
Factorise $: a^4- 1$
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Answer

$a^4 - 1$
$= ( a^2 )^2 - ( 1 )^2$
$= ( a^2 + 1 )( a^2 - 1 ) [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( a^2 + 1 )[ (a)^2 - (1)^2]$
$= ( a^2 + 1 )( a + 1 )( a - 1 )$

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