206 Вправа 206Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 59

206. Спростіть вираз:

1) ${\displaystyle a^2-ab=}$${\displaystyle a(a-b)}$; ${\displaystyle b^2-ab=}$${\displaystyle -b(a-b)}$;

${\displaystyle \frac{{1+a}^{\mathrm{\setminus }b}}{a(a-b)}+\frac{{1-b}^{\mathrm{\setminus }a}}{b(a-b)}=}$${\displaystyle \frac{(1+a)\cdot b}{ab(a-b)}+\frac{(1-b)\cdot a}{ab(a-b)}=}$${\displaystyle \frac{(1+a)b+(1-b)a}{ab(a-b)}=}$${\displaystyle \frac{b+ab+a-ab}{ab(a-b)}=}$${\displaystyle \frac{a+b}{ab(a-b)}}$;

${\displaystyle \frac{a+b}{ab(a-b)}\cdot \frac{ab(a-b)}{a+b}=}$${\displaystyle 1}$;

2) ${\displaystyle \frac{3{\left(x^{2}y\right)}^3}{{\left(3a{c}^2\right)}^2}=}$${\displaystyle \frac{3x^6{y}^3}{9a^2{c}^4}=}$${\displaystyle \frac{x^6{y}^3}{3a^2{c}^4}}$;

${\displaystyle {\left(\frac{x^6{y}^3}{3a^2{c}^4}\right)}^2\cdot \frac{a^3{c}^4}{15x^3{y}^4}=}$${\displaystyle \frac{x^{12}{y}^6}{9a^4{c}^8}\cdot \frac{a^3{c}^4}{15x^3{y}^4}=}$${\displaystyle \frac{x^9{y}^2}{135a{c}^4}}$.