Find the expression for the product $(x + a) (x + b) (x + c)$ using the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$

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Solution

$(x + a) (x + b) (x + c)$
$= [x^{2} + (a + b) x + a b] (x + c)$
$= x^{2} (x + c) + [(a + b) x + a b] (x + c)$
$= x^{3} + x^{2} c + a x^{2} + b x^{2} + a c x + b c x + a b x + a$
$= x^{3} + (a + b + c) x^{2} + (a b + b c + c a) x + a b c$

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