Find K in the expansion (m-2n) ^10.

M^10 - 20m^9 n + km^8 n^2 - ... + 1024 n^10

10 10 10 10

(m-2n) ¹⁰ = (0) m¹⁰n⁰ - (1) m¹⁰ (2n) ¹ + (2) m⁸ (2n) ² + ... + (10) m° (2n) ¹⁰

10

km⁸n² = (2) m⁸ (2n) ²

10

(2) = 10! / (10-2) !2!=10.9.8! / (8!.2!) = 45

(2n) ²=4n²

Then:

Km⁸n²=45m⁸ (4n²)

Km⁸n²=180m⁸n²

K=180

answer: K=180