Mathematics
Factorise :
(a2 - 3a)(a2 - 3a + 7) + 10
Factorisation
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Answer
Given,
(a2 - 3a)(a2 - 3a + 7) + 10
Substituting a2 - 3a = x, we get :
⇒ x(x + 7) + 10
= x2 + 7x + 10
= x2 + 2x + 5x + 10
= x(x + 2) + 5(x + 2)
= (x + 5)(x + 2)
= (a2 - 3a + 5)(a2 - 3a + 2)
= (a2 - 3a + 5)(a2 - 2a - a + 2)
= (a2 - 3a + 5)[a(a - 2) -1(a - 2)]
= (a2 - 3a + 5)(a - 1)(a - 2)
Hence, (a2 - 3a)(a2 - 3a + 7) + 10 = (a2 - 3a + 5)(a - 1)(a - 2).
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