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

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Solution

$(x + 2)^{3} + (x - 2)^{3} = (x + 2 + - 2) [(x + 2)^{2} - (x + 2) (x - 2) + (x - 2)^{2}] = 2 x [x^{2} + 4 x + 4 - (x^{2} + 2 x - 2 x - 4) + x^{2} - 4 x + 4] = 2 x [x^{2} + 4 x + 4 - x^{2} - 2 x + 2 x + 4 + 6 x^{2} - 4 x + 4] = 2 x [x^{2} + 12]$

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