Find the products:
(a) $(x + 1) (3 x^{2} - x^{3} + x + 1)$
(b) $(x + y) (x^{2} - x y + y^{2})$

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Solution

(a) $(x + 1) (3 x^{2} - x^{3} + x + 1)$
$= 3 x^{3} - x^{4} + x^{2} + x + 3 x^{2} - x^{3} + x + 1$
$= 2 x^{3} - X^{4} + x^{2} + 2 x + 1$
$= - x^{4} + 2 x^{3} + x^{2} + 2 x + 1$

(b) $(x + y) (x^{2} - x y + y^{2})$
$= x^{3} - x^{2} y + x y^{2} + y x^{2} - x y^{2} + y^{3}$
$= x^{3} + y^{3}$

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