Question

find coefficient of x^5 in the expansion of the product of (1+x)^3(1-x)^6

Answer 1

coefficient of x⁵ in above expression is -6.

(1+ x)³  (1-x)⁶ = (1 + 3x + 3x² + x³)  (1 - 6x + 15x² - 20 x³ + 15x⁴ - 6x⁵ + x⁶).
Now adding coefficients of x⁵ we get coefficient = -6.