Question 6

A factor of $$\sum a^2 b + \sum ab^2 + 3abc$$ is ($$a$$, $$b$$, $$c$$ are real numbers)

Solution

Expanding, $$(a + b + c)(ab + bc + ca) = a^2b + b^2c + c^2a + ab^2 + bc^2 + ca^2 + 3abc = \sum a^2 b + \sum ab^2 + 3abc$$. So the expression equals $$\left(\sum a\right)\left(\sum ab\right)$$, and both $$\sum a$$ and $$\sum ab$$ are factors. Hence options b and c are both correct.

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