395° Вправа 395Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 110

395. Запишіть як квадрат двочлена:

${\displaystyle A^2-2AB+B^2=}$${\displaystyle {(A-B)}^2}$.

1) ${\displaystyle y^{-2}-4y^{-1}+4=}$${\displaystyle {\left(y^{-1}\right)}^2-2\cdot y^{-1}\cdot 2+2^2=}$${\displaystyle {\left(y^{-1}-2\right)}^2}$;

2) ${\displaystyle x^{-2}-2{\left(xy\right)}^{-1}+y^{-2}=}$${\displaystyle {\left(x^{-1}\right)}^2-2\cdot x^{-1}\cdot y^{-1}+{\left(y^{-1}\right)}^2=}$${\displaystyle {\left(x^{-1}-y^{-1}\right)}^2}$;

3) ${\displaystyle a^{-4}-10a^{-2}+25=}$${\displaystyle {\left(a^{-2}\right)}^2-2\cdot a^{-2}\cdot 5+5^2=}$${\displaystyle {\left(a^{-2}-5\right)}^2}$;

4) ${\displaystyle 4m^{-2}-12m^{-1}{n}^{-1}+9n^{-2}=}$${\displaystyle {\left(2m^{-1}\right)}^2-2\cdot 2m^{-1}\cdot 3n^{-1}+{\left(3n^{-1}\right)}^2=}$${\displaystyle {\left(2m^{-1}-3n^{-1}\right)}^2}$;

5) ${\displaystyle a^{-2}{c}^{-4}-2a^{-1}{c}^{-2}+1=}$${\displaystyle {\left(a^{-1}{c}^{-2}\right)}^2-2\cdot a^{-1}{c}^{-2}\cdot 1+1^2=}$${\displaystyle {\left(a^{-1}{c}^{-2}-1\right)}^2}$;

6) ${\displaystyle 9a^{-2}{b}^{-2}-6a^{-1}{b}^{-2}{c}^{-1}+c^{-2}{b}^{-2}=}$${\displaystyle {\left(3a^{-1}{b}^{-1}\right)}^2-2\cdot 3a^{-1}{b}^{-1}\cdot b^{-1}{c}^{-1}+{\left(b^{-1}{c}^{-1}\right)}^2=}$${\displaystyle {\left(3a^{-1}{b}^{-1}-b^{-1}{c}^{-1}\right)}^2}$.