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1)

$(a+1)^4 + a^4 + 1^4 = 2(a^4 + 2a^3 + 3a^2 + 2a + 1) $


$(a+1)^2 + a^2 + 1^2 = 2(a^2 + a + 1) $



$\frac{(a+1)^4 + a^4 + 1^4}{(a+1)^2 + a^2 + 1^2} = a^2 + a + 1$


$(2^2 + 2 + 1) + (3^2 + 3 + 1) + ... + (10^2 + 10 + 1)$