№ 5.11 Алгебра = № 10.11 Математика
Виконайте множення:
1. $ \frac{a^2+2a}{5}\cdot\frac{a}{4a+8};$
2. $\frac{7m}{a}\cdot\frac{a^2-ab}{21};$
3. $ \frac{2a-b}{10a}\cdot\frac{15a^2}{b-2a};$
4. $ \frac{10ab}{x+y}\cdot\frac{x^2-y^2}{5ab};$
5. $-\frac{ab-ac}{10p}\cdot\frac{25p}{xc-xb};$
6. $\frac{a^2+ab}{x^2}\cdot\frac{xy}{a^2+2ab+b^2}.$
Розв'язок:
1. $ \frac{a^2+2a}{5}\cdot\frac{a}{4a+8}=\frac{a\left(a+2\right)\cdot a}{5\cdot4\left(a+2\right)}=\frac{a^2}{20};$
2. $\frac{7m}{a}\cdot\frac{a^2-ab}{21}=\frac{7m\cdot a\left(a-b\right)}{a\cdot21}=$
$= \frac{7m\left(a-b\right)}{21}=\frac{m\left(a-b\right)}{3};$
3. $ \frac{2a-b}{10a}\cdot\frac{15a^2}{b-2a}=\frac{\left(2a-b\right)\cdot15a^2}{-10a\left(2a-b\right)}=$
$= -\frac{15a}{10}=-\frac{3a}{2};$
4. $ \frac{10ab}{x+y}\cdot\frac{x^2-y^2}{5ab}=\frac{10ab\left(x-y\right)\left(x+y\right)}{\left(x+y\right)\cdot5ab}=$
$= \frac{2\left(x-y\right)}{1}=2\left(x-y\right);$
5. $-\frac{ab-ac}{10p}\cdot\frac{25p}{xc-xb}=$
$= -\frac{a\left(b-c\right)\cdot25p}{10p\cdot(-x\left(b-c\right))}=\frac{5a}{2x};$
6. $\frac{a^2+ab}{x^2}\cdot\frac{xy}{a^2+2ab+b^2}=$
$= \frac{a\left(a+b\right)\cdot x y}{x^2\cdot\left(a+b\right)^2}=\frac{ay}{x\left(a+b\right)}.$