Question 3(v)
Simplify:
$(x + y) (x^{2} - x y + y^{2})$

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Solution

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

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

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(x + y) (x^{2} - x y + y^{2})

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