396° Вправа 396Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 110

396. Розкладіть на множники:

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

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

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

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

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

5) ${\displaystyle n^{-4}-m^6=}$${\displaystyle {\left(n^{-2}\right)}^2-{\left(m^3\right)}^2=}$${\displaystyle \left(n^{-2}-m^3\right)\left(n^{-2}+m^3\right)}$;

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

7) ${\displaystyle {(x^{-2}+y^{-2})}^2-{(x^{-2}-y^{-2})}^2=}$${\displaystyle (x^{-2}+y^{-2}-x^{-2}+y^{-2})(x^{-2}+y^{-2}+x^{-2}-y^{-2})=}$${\displaystyle 2y^{-2}\cdot 2x^{-2}=}$${\displaystyle 4x^{-2}{y}^{-2}}$;

8) ${\displaystyle {(2+m^{-2})}^2-{(2-m^{-2})}^2=}$${\displaystyle (\cancel{2}+m^{-2}\cancel{-2}+m^{-2})(2+\cancel{m^{-2}}+2\cancel{-m^{-2}})=}$${\displaystyle 2m^{-2}\cdot 4=}$${\displaystyle 8m^{-2}}$.