Factorise the expression , ${(x + y + z)}^{3} - x^{3} - y^{3} - z^{3}$ into linear factors.

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Solution

$(x + y + z)^{3} - x^{3} - y^{3} - z^{3} (x + y + z - x) ((x + y + z)^{2} + x^{2} + x (x + y + z)) - (y + z) (y^{2} + z^{2} - y z) (y + z) [3 x^{2} + 3 x y + 3 x z] 3 x (y + z) (x + y + z)$
Thus the three factors are
$(3 x), (x + y + z), (y + z)$

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