652 Вправа 652Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 193

652. Спростіть вираз:

1) ${\displaystyle {(\sqrt{a}+2)}^2+{(\sqrt{a}-2)}^2=}$${\displaystyle ({\left(\sqrt{a}\right)}^2+2\cdot \sqrt{a}\cdot 2+2^2)+({\left(\sqrt{a}\right)}^2-2\cdot \sqrt{a}\cdot 2+2^2)=}$${\displaystyle a+4\sqrt{a}+4+a-4\sqrt{a}+4=}$${\displaystyle 2a+8}$;

2) ${\displaystyle {(\sqrt{y}-\sqrt{x})}^2-(\sqrt{y}+\sqrt{x})(\sqrt{y}-\sqrt{x})=}$${\displaystyle ({\left(\sqrt{y}\right)}^2-2\sqrt{y}\sqrt{x}+{\left(\sqrt{x}\right)}^2)-({\left(\sqrt{y}\right)}^2-{\left(\sqrt{x}\right)}^2)=}$${\displaystyle y-2\sqrt{xy}+x-(y-x)=}$${\displaystyle y-2\sqrt{xy}+x-y+x=}$${\displaystyle 2x-2\sqrt{xy}}$.