Mathematics
Factorise :
9a2 - (a2 - 4)2
Factorisation
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Answer
Given,
9a2 - (a2 - 4)2
= (3a)2 - (a2 - 4)2
= (3a + a2 - 4)[3a - (a2 - 4)]
= (a2 + 3a - 4)(4 - a2 + 3a)
= (a2 + 4a - a - 4).-(a2 - 3a - 4)
= [a(a + 4) - 1(a + 4)].-[a2 - 4a + a - 4]
= (a + 4)(a - 1).-[a(a - 4) + 1(a - 4)]
= (a + 4)(a - 1).-(a - 4)(a + 1)
= (a + 4)(a - 1)(4 - a)(a + 1).
Hence, 9a2 - (a2 - 4)2 = (a + 4)(a - 1)(4 - a)(a + 1).
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