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Question
Factorize : 9a2 - (a2 - 4) 2
Sum
Solution
9a2 - (a2 - 4)2
= (3a)2 - (a2 - 4)2
= [ 3a + (a2 - 4)][ 3a - (a2 - 4)]
= [ 3a + a2 - 4 ][ 3a - a2 + 4 ]
= [ a2 + 3a - 4 ][- a2 + 3a + 4]
= (a + 4)(a - 1)(-a2 + 3a + 4)
= (a + 4)(a - 1)[-(a2 - 3a - 4)]
= - (a + 4)(a - 1)(a - 4)(a + 1)
= (a + 4)(a - 1)(a + 1)(4 - a).
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Method of Factorisation : Difference of Two Squares
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