Simplify the following:

$(i) (a^{2} + b^{2} + c^{2}) (2 a + 3 b)$

$(i i) (p + q) (p^{2} - p q + q^{2})$

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Solution

$(i) (a^{2} + b^{2} + c^{2}) (2 a + 3 b)$

$= 2 a^{3} + 2 a b^{2} + 2 a c^{2} + 3 a^{2} b + 3 b^{3} + 3 b c^{2}$

$(i i) (p + q) (p^{2} - p q + q^{2})$

$= p^{3} - p^{2} q + p q^{2} + q p^{2} - p q^{2} + q^{3}$

$= p^{3} + q^{3}$

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