Find the coefficient of x² in the expansion of

(x² + x + 1)² + (x² - x + 1)².

The above equation can be written as,

$(x^2 + x + 1)^2 + (x^2 - x + 1)^2 = {(x^2 + 1) + x}^2 + {(x^2 + 1) - x}^2 \\[1em] = 2{(x^2 + 1)^2 + x^2} \\[1em] = 2{(x^2)^2 + 1 + 2x^2 + x^2} \\[1em] = 2{x^4 + 3x^2 + 1} \\[1em] = 2x^4 + 6x^2 + 2.$

Hence, coefficient of x² = 6.