Determine the variables in the expression $x^{7} + 7 x y z + y^{7} + z^{7} + 7$ .

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Solution

Now given the expression is $x^{7} + 7 x y z + y^{7} + z^{7} + 7$ .
From this it is clear that the variables occurring in the expression are $x, y, z$ .

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Show that: ${(x + y)}^{7} - x^{7} - y^{7} = 7 x y (x + y) {(x^{2} + x y + y^{2})}^{2}$ .

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