231 Вправа 231Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 66

231. Спростіть вираз.

1) ${\displaystyle \frac{(x^2-y^2)(x^2+y^2)}{{(x-y)}^2}\cdot \frac{{\left(x-y\right)}^2}{x+y}=}$${\displaystyle \frac{(x-y)\cancel{\left(x+y\right)}(x^2+y^2)\cancel{{\left(x-y\right)}^2}}{\cancel{{\left(x-y\right)}^2}\cancel{\left(x+y\right)}}=}$${\displaystyle \left(x^2+y^2\right)\left(x-y\right)}$;

2) ${\displaystyle \frac{a^2-ab+b^2}{(x-y)(x+y)}\cdot \frac{{\left(x-y\right)}^2}{\left(a+b\right)\left(a^2-ab+b^2\right)}=}$${\displaystyle \frac{\cancel{\left(a^2-ab+b^2\right)}\cancel{\left(x-y\right)}(x-y)}{\cancel{\left(x-y\right)}(x+y)(a+b)\cancel{\left(a^2-ab+b^2\right)}}=}$${\displaystyle \frac{x-y}{\left(x+y\right)\left(a+b\right)}}$.