225 Вправа 225Алгебра 8 клас Бевз 2025 · § 5 · стор. 50

225. Виконай множення.

а) ${\displaystyle \frac{2,7}{2x^2}\cdot \frac{20}{9x^3}=}$${\displaystyle \frac{2,7\cdot 20}{2x^2\cdot 9x^3}=}$${\displaystyle \frac{3\cdot \cancel{18}}{\cancel{18}{x}^5}=}$${\displaystyle \frac{3}{x^5}}$;

б) ${\displaystyle \frac{1}{4a^3}\cdot \frac{-2a}{7c}=}$${\displaystyle \frac{-2a}{4a^3\cdot 7c}=}$${\displaystyle -\frac{\cancel{2}\cancel{a}}{2\cdot \cancel{2}{a}^2\cancel{a}\cdot 7c}=}$${\displaystyle -\frac{1}{14a^{2}c}}$;

в) ${\displaystyle \frac{2ab}{-5a^2}\cdot \frac{5c^2}{4a^2{b}^3}=}$${\displaystyle \frac{2ab\cdot 5c^2}{-5a^2\cdot 4a^2{b}^3}}$=

=${\displaystyle -\frac{\cancel{2}\cancel{a}\cancel{b}\cdot \cancel{5}{c}^2}{\cancel{5}a\cancel{a}\cdot 2\cdot \cancel{2}{a}^2{b}^2\cancel{b}}=}$${\displaystyle -\frac{c^2}{2a^3{b}^2}}$;

г) ${\displaystyle 2m^2\cdot \frac{n}{8m}=}$${\displaystyle \frac{2m^2\cdot n}{8m}=}$${\displaystyle \frac{\cancel{2}m\cancel{m}\cdot n}{4\cdot \cancel{2}\cancel{m}}=}$${\displaystyle \frac{mn}{4}}$;

ґ) ${\displaystyle \frac{-b}{12ac}\cdot 4a{c}^2=}$${\displaystyle \frac{-b\cdot 4a{c}^2}{12ac}=}$${\displaystyle -\frac{b\cdot \cancel{4}\cancel{a}c\cancel{c}}{3\cdot \cancel{4}\cancel{a}\cancel{c}}=}$${\displaystyle -\frac{bc}{3}}$;

д) ${\displaystyle \frac{5a^2}{3b{c}^2}\cdot (-6a{c}^3)=}$${\displaystyle \frac{5a^2\cdot (-6a{c}^3)}{3b{c}^2}}$=

=${\displaystyle -\frac{5a^2\cdot 2\cdot \cancel{3}ac\cancel{c^2}}{\cancel{3}b\cancel{c^2}}=}$${\displaystyle -\frac{10a^{3}c}{b}}$.