Mathematics

Factorise :

9(a - 2)2 - 16(a + 2)2

Factorisation

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Answer

Given,

   9(a - 2)2 - 16(a + 2)2

= {[3(a - 2)]2 - [4(a + 2)]2}

= {[3(a - 2) + 4(a + 2)][3(a - 2) - 4(a + 2)]}

= [(3a - 6 + 4a + 8)(3a - 6 - 4a - 8)]

= (7a + 2)(-a - 14)

= -(7a + 2)(a + 14).

Hence, 9(a - 2)2 - 16(a + 2)2 = -(7a + 2)(a + 14).

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