Mathematics
Factorise :
a6 - 7a3 - 8
Factorisation
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Answer
Given,
a6 - 7a3 - 8
= (a3)2 - 7a3 - 8
Substituting a3 = x, we get :
= x2 - 7x - 8
= x2 - 8x + x - 8
= x(x - 8) + 1(x - 8)
= (x - 8)(x + 1)
= (a3 - 8)(a3 + 1)
= (a3 - 23)(a3 + 13)
= (a - 2)(a2 + a × 2 + 22)(a + 1)(a2 - a × 1 + 12)
= (a - 2)(a2 + 2a + 4)(a + 1)(a2 - a + 1)
= (a - 2)(a + 1)(a2 + 2a + 4)(a2 - a + 1).
Hence, a6 - 7a3 - 8 = (a - 2)(a + 1)(a2 + 2a + 4)(a2 - a + 1).
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