№ 5.12 Алгебра = № 10.12 Математика
Виконайте множення:
1. $ \frac{m^2-3m}{7}\cdot\frac{x}{2m-6};$
2. $\frac{5a}{x^2+xy}\cdot\frac{x}{15};$
3. $ \frac{a-b}{16m^2}\cdot\frac{24m}{b-a};$
4. $ \frac{x^2-y^2}{5pc}\cdot\frac{20pc}{x-y};$
5. $\frac{3a-3b}{12x}\cdot\left(-\frac{18x}{mb-ma}\right);$
6. $\frac{m^2-2mn+n^2}{pc}\cdot\frac{p^2}{m^2-mn}.$
Розв'язок:
1. $ \frac{m^2-3m}{7}\cdot\frac{x}{2m-6}=\frac{m\left(m-3\right)\cdot x}{7\cdot2\left(m-3\right)}=$
$= \frac{mx}{14};$
2. $\frac{5a}{x^2+xy}\cdot\frac{x}{15}=\frac{5ax}{x\left(x+xy\right)\cdot15}=$
$= \frac{a}{3\left(x+y\right)};$
3. $ \frac{a-b}{16m^2}\cdot\frac{24m}{b-a}=\frac{\left(a-b\right)\cdot24m}{-16m^2\left(a-b\right)}=$
$= -\frac{3}{2m};$
4. $ \frac{x^2-y^2}{5pc}\cdot\frac{20pc}{x-y}=$
$= \frac{\left(x-y\right)\left(x+y\right)\cdot20pc}{5pc\cdot\left(x-y\right)}=$
$= \frac{4\left(x+y\right)}{1}=4\left(x+y\right);$
5. $\frac{3a-3b}{12x}\cdot\left(-\frac{18x}{mb-ma}\right)=$
$= -\frac{3\left(a-b\right)\cdot18x}{12x\cdot(-m\left(a-b\right))}=\frac{9}{2m};$
6. $\frac{m^2-2mn+n^2}{pc}\cdot\frac{p^2}{m^2-mn}=$
$= \frac{\left(m-n\right)^2\cdot p^2}{pc\cdot m\left(m-n\right)}=\frac{\left(m-n\right)p}{cm}.$