467 Вправа 467Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

467. Спрости вираз.

а) ${\displaystyle {(x-y)}^{-2}(x^2-y^2)}$;

${\displaystyle \frac{(x-y)(x+y)}{{(x-y)}^2}=}$${\displaystyle \frac{\cancel{\left(x-y\right)}(x+y)}{\cancel{\left(x-y\right)}(x-y)}=}$${\displaystyle \frac{x+y}{x-y}}$;

б) ${\displaystyle {(a^{-3}-b^{-3})}^{-1}-{(a^{-3}+b^{-3})}^{-1}}$;

1) ${\displaystyle {(a^{-3}-b^{-3})}^{-1}=}$${\displaystyle {\left(\frac{b^3-a^3}{a^3{b}^3}\right)}^{-1}=}$${\displaystyle \frac{a^3{b}^3}{b^3-a^3}}$;

2) ${\displaystyle {(a^{-3}+b^{-3})}^{-1}=}$${\displaystyle \frac{a^3{b}^3}{b^3+a^3}}$;

3) ${\displaystyle \frac{a^3{b}^3}{b^3-a^3}-\frac{a^3{b}^3}{b^3+a^3}=}$${\displaystyle \frac{a^3{b}^3(b^3+a^3-b^3+a^3)}{b^6-a^6}=}$${\displaystyle \frac{2a^6{b}^3}{b^6-a^6}}$;

в) ${\displaystyle {(a^{-1}+b^{-1})}^2-{(a^{-1}-b^{-1})}^2}$;

${\displaystyle (a^{-1}+b^{-1}-a^{-1}+b^{-1})(a^{-1}+b^{-1}+a^{-1}-b^{-1})}$=

=${\displaystyle 2b^{-1}\cdot 2a^{-1}=}$${\displaystyle \frac{4}{ab}}$;

г) ${\displaystyle {(p^{-3}+p^3)}^2-p^{-6}-2}$;

${\displaystyle p^{-6}+2+p^6-p^{-6}-2=}$${\displaystyle p^6}$.