In the expansion of (x − y)¹⁵, calculate the coefficient of x³y¹² and x²y¹³.

The coefficient of x³y¹² is positive because the exponent of y is even. The coefficient is ¹⁵C₁₂.

¹⁵C₁₂ = ^15!/_{12! × 3!} = (15 × 14 × 13 × 12!)/(12! × 6) = 455

The coefficient of x²y¹³ is negative because the exponent of y is odd. The coefficient is −¹⁵C₁₃.

(−¹⁵C₁₃) = −(15 × 14)/(2 × 1) = −15 × 7 = −105

Hence, coefficients are:

x³y¹² → +455
x²y¹³ → −105