230 Вправа 230Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 66

230. Спростіть вираз.

1) ${\displaystyle \frac{(x+y)(x^2-xy+y^2)}{x-y}\cdot \frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x+y}=}$${\displaystyle (x^2-xy+y^2)(x^2+xy+y^2)=}$${\displaystyle {(x^2+y^2)}^2-x^2{y}^2=}$${\displaystyle x^4+x^2{y}^2+y^4}$;

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