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Question
Factorise the following:
(y2 - 3y)(y2 - 3y + 7) + 10
Solution
(y2 - 3y)(y2 - 3y + 7) + 10
= a(a + 7) + 10 [taking (y2 - 3y) = a]
= a2 + 7a + 10
= a2 + 5a + 2a + 10
= a(a + 5) + 2(a + 5)
= (a + 5)(a + 2)
= (y2 - 3y + 5)(y2 - 3y + 2)
= (y2 - 3y + 5)(y2 - 2y - y + 2)
= (y2 - 3y + 5)[y(y - 2) - 1(y - 2)]
= (y2 - 3y + 5)[(y - 2)(y - 1)]
= (y - 1)(y - 2)(y2 - 3y + 5).
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