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Factorise: (a2 – 2d)2 – 23(a2 – 2d) + 120 |
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Answer» Let a2 – 2a = x (a2 – 2d)2 – 23 (a2 – 2d) + 120 = x2 – 23x + 120 = x2 – 15x – 8x + 120 = x(x – 15) – 8(x – 15) = (x – 15)(x – 8) = (a2 – 2a – 15)(a2 – 2a – 8) [Put x = a2 – 2a] = (a2 – 5a + 3a – 15) (a2 – 4a + 2a – 8) = [a(a – 5) + 3(a – 5)] x [a(a – 4) + 2(a – 4)] = (a – 5) (a + 3) x (a – 4) (a + 2) = (a + 2) (a + 3) (a – 4) (a – 5) |
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