407 Вправа 407Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 112

407. Дано вираз: x⁻⁴ + x⁻³ + x⁻² + x⁻¹ + 1. Винесіть за дужки:

${\displaystyle X=}$${\displaystyle x^{-4}+x^{-3}+x^{-2}+x^{-1}+1}$; ${\displaystyle x^n:x^k=}$${\displaystyle x^{n-k}}$.

1) ${\displaystyle X=}$${\displaystyle x\left(x^{-5}+x^{-4}+x^{-3}+x^{-2}+x^{-1}\right)}$;

2) ${\displaystyle X=}$${\displaystyle x^6\left(x^{-10}+x^{-9}+x^{-8}+x^{-7}+x^{-6}\right)}$;

3) ${\displaystyle X=}$${\displaystyle x^{-1}\left(x^{-3}+x^{-2}+x^{-1}+1+x\right)}$;

4) ${\displaystyle X=}$${\displaystyle x^{-4}\left(1+x+x^2+x^3+x^4\right)}$;

5) ${\displaystyle X=}$${\displaystyle x^{-5}\left(x+x^2+x^3+x^4+x^5\right)}$;

6) ${\displaystyle X=}$${\displaystyle x^{-10}\left(x^6+x^7+x^8+x^9+x^{10}\right)}$.