Find the expansion of
(x – a)(x – 2a)(x – 4a)
(x – a)(x – 2a)(x – 4a)
Here we have to use the identity
(x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
∴ (x – a)(x – 2a)(x – 4a)
= x3 + (– a – 2a – 3a)x2 + [(– a)(– 2a) + (– 2a)(– 3a) + (– 3a)(– a)]x + (– a)(– 2a)(– 3a)
= x3 – 6ax2 + (2a2 + 6a2 + 3a2)x – 6a3
= x3 – 6ax2 + 11a2x – 6a3
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