1²+3²+4² + ... + (2n-2) ² = ⅓n (2n-1) (2n+1)

1² + 3² + 4² + 4 (n - 1) ² = ¹/₃n (2n - 1) (2n + 1)

1² + 3² + 4² + (2n - 2) ² = ¹/₃n (2n - 1) (2n + 1)

1 + 9 + 16 + (2n - 2) (2n - 2) = ¹/₃n (2n (2n + 1) - 1 (2n + 1))

10 + 16 + (2n (2n - 2) - 2 (2n - 2)) = ¹/₃n (2n (2n) + 2n (1) - 1 (2n) - 1 (1) 16 + (2n (2n) - 2n (2) - 2 (2n) + 2 (2)) = ¹/₃n (4n² + 2n - 2n - 1)

26 + (4n² - 4n - 4n + 4) = ¹/₃n (4n² - 1)

26 + (4n² - 8n + 4) = ¹/₃n (4n² - 1)

26 + 4n² - 8n + 4 = ¹/₃n (4n²) - ¹/₃n (1)

4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n

4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n

+ ¹/₃n + ¹/₃n

4n² - 7²/₃n + 30 = 1¹/₃n³

-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0

-3 (-1¹/₃n³ + 4n² - 7²/₃n + 30) = - 3 (0)

-3 (-1¹/₃n³) - 3 (4n²) - 3 (-7²/₃n) - 3 (30) = 0

4n³ - 12n² + 23n - 90 = 0