227 Вправа 227Алгебра 8 клас Бевз 2025 · § 5 · стор. 51

227. Виконай множення.

а) ${\displaystyle \frac{a+b}{x}\cdot \frac{3x^2}{2(a+b)}=}$${\displaystyle \frac{(a+b)\cdot 3x^2}{x\cdot 2(a+b)}=}$${\displaystyle \frac{3\cancel{x}x\cancel{\left(a+b\right)}}{2\cancel{x}\cancel{\left(a+b\right)}}=}$${\displaystyle \frac{3x}{2}}$;

б) ${\displaystyle \frac{1}{x^2-y^2}\cdot \frac{x-y}{4xy}=}$${\displaystyle \frac{x-y}{(x^2-y^2)\cdot 4xy}}$=

=${\displaystyle \frac{\cancel{\left(x-y\right)}}{4xy(x+y)\cancel{\left(x-y\right)}}=}$${\displaystyle \frac{1}{4xy\left(x+y\right)}}$;

в) ${\displaystyle \frac{3}{x^2-y^2}\cdot \frac{{(x+y)}^2}{3}=}$${\displaystyle \frac{3\cdot {(x+y)}^2}{(x^2-y^2)\cdot 3}}$=

=${\displaystyle \frac{\cancel{3}\cancel{\left(x+y\right)}(x+y)}{\cancel{3}\cancel{\left(x+y\right)}(x-y)}=}$${\displaystyle \frac{x+y}{x-y}}$;

г) ${\displaystyle \frac{a^2-ab}{m^3}\cdot \frac{m^2}{a-b}=}$${\displaystyle \frac{(a^2-ab)\cdot m^2}{m^3\cdot (a-b)}=}$${\displaystyle \frac{a\cancel{m^2}\cancel{\left(a-b\right)}}{\cancel{m^2}m\cancel{\left(a-b\right)}}=}$${\displaystyle \frac{a}{m}}$;

ґ) ${\displaystyle \frac{3ax}{ax+ac}\cdot \frac{cx+c^2}{9x}=}$${\displaystyle \frac{3ax\cdot (cx+c^2)}{(ax+ac)\cdot 9x}=}$${\displaystyle \frac{\cancel{3}\cancel{a}\cancel{x}c\cancel{\left(x+c\right)}}{3\cdot \cancel{3}\cancel{a}\cancel{x}\cancel{\left(x+c\right)}}=}$${\displaystyle \frac{c}{3}}$;

д) ${\displaystyle \frac{6m}{a^2-a}\cdot \frac{2a-2}{9m^2}=}$${\displaystyle \frac{6m\cdot (2a-2)}{(a^2-a)\cdot 9m^2}=}$${\displaystyle \frac{4\cdot \cancel{3}\cancel{m}\cancel{\left(a-1\right)}}{3\cdot \cancel{3}\cancel{m}ma\cancel{\left(a-1\right)}}=}$${\displaystyle \frac{4}{3ma}}$.