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प्रश्न
Factorise: 5 - (3a2 - 2a) (6 - 3a2 + 2a)
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उत्तर
5 - (3a2 - 2a) (6 - 3a2 + 2a)
= 5 - (3a2 - 2a)[6 - (3a2 - 2a)]
Assume that 3a2 - 2a = x
Therefore,
5 - (3a2 - 2a)(6 - 3a2 + 2a)
= 5 - x(6 - x)
= 5 - 6x + x2
= x2 - (5 + 1)x + 5
= x2 - 5x - 1x + 5
= x(x - 5) -1 (x - 5)
= (x - 5) (x - 1)
put x = 3a2 - 2a
= (3a2 - 2a - 5) (3a2 - 2a - 1)
= (3a2 - 5a + 3a - 5) (3a2 - 3a + a - 1)
= [a(3a - 5) + 1(3a - 5)] [3a(a - 1) + 1(a - 1)]
= (3a - 5) (a + 1) (3a + 1) (a - 1)
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