Use the Binomial Theorem to find the coefficient of x8 in th

Use the Binomial Theorem to find the coefficient of x^8 in the expansion of (x^2 -3)^7

Solution

(x² - 3)⁷ = (y-3)⁷ using y = x²

(x² - 3)⁷ = y⁷ + 7y⁶ x 3 + 21y⁵ x 3² + 35y⁴ x 3³ + 35y³ x 3⁴ + 21y² x 3⁵ + 7y x 3⁶ + 3⁷

cofficient of x⁸ = coefficient of y⁴ = 35 x 9 = 315