Вправи: 240-241

240. Винесіть за дужки Зⁿ:

1) Зⁿ + 3ⁿ⁺⁶ = 3ⁿ(1 + 3^n+6–n) = 3ⁿ(1 + 3⁶) = 730 • 3ⁿ;

2) 3ⁿ – 2 • 3²⁺ⁿ = 3ⁿ(3^n–n – 2 • З^2+n–n) = 3ⁿ(3⁰ – 2 • З²) = 3ⁿ(1 – 18) = –17 • 3ⁿ;

3) Зⁿ⁺⁵ + Зⁿ⁺¹ = 3ⁿ(3^n+5–n + 3^n+1–n) = 3ⁿ(3⁵ + 3) = 246 • 3ⁿ.

241. Винесіть за дужки 2ⁿ:

1) 2ⁿ + 2ⁿ⁺¹ = 2ⁿ(2^n–n + 2^n+1–n) = 2ⁿ(2⁰ + 2) = 3 • 2ⁿ;

2) 2ⁿ – 5 • 2ⁿ⁺⁶ = 2ⁿ(1 – 5 • 2^n+6–n) = 2ⁿ(1 – 5 • 2⁶) = 2ⁿ(1 – 320) = –319 • 2ⁿ;

3) 2ⁿ⁺² – 3 • 2ⁿ⁺³ = 2ⁿ(2^n+2–n – 3 • 2^n+3–n) = 2ⁿ(2² – 3 • 2³) = 2ⁿ(4 – 24) = –20 • 2ⁿ.