826 Вправа 826Алгебра 8 клас Бевз 2025 · § 16 · стор. 155

826. Розклади на множники вираз.

Використовуємо ${\displaystyle a=}$${\displaystyle {\left(\sqrt{a}\right)}^2}$ (${\displaystyle a\ge 0}$) і формули скороченого множення.

а) ${\displaystyle \sqrt{35}-\sqrt{5}=}$${\displaystyle \sqrt{5}\cdot \sqrt{7}-\sqrt{5}=}$${\displaystyle \sqrt{5}\left(\sqrt{7}-1\right)}$;

б) ${\displaystyle 7-\sqrt{7}=}$${\displaystyle \sqrt{7}\cdot \sqrt{7}-\sqrt{7}=}$${\displaystyle \sqrt{7}\left(\sqrt{7}-1\right)}$;

в) ${\displaystyle x\sqrt{y}-\sqrt{x}=}$${\displaystyle \sqrt{x}\cdot \sqrt{x}\sqrt{y}-\sqrt{x}=}$${\displaystyle \sqrt{x}\left(\sqrt{xy}-1\right)}$;

г) ${\displaystyle 4a^2-3}$=

=${\displaystyle {\left(2a\right)}^2-{\left(\sqrt{3}\right)}^2=}$${\displaystyle \left(2a-\sqrt{3}\right)\left(2a+\sqrt{3}\right)}$;

ґ) ${\displaystyle m^2-n=}$${\displaystyle m^2-{\left(\sqrt{n}\right)}^2=}$${\displaystyle \left(m-\sqrt{n}\right)\left(m+\sqrt{n}\right)}$;

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

е) ${\displaystyle a-2\sqrt{ab}+b}$=

=${\displaystyle {\left(\sqrt{a}\right)}^2-2\sqrt{a}\sqrt{b}+{\left(\sqrt{b}\right)}^2=}$${\displaystyle {\left(\sqrt{a}-\sqrt{b}\right)}^2}$;

є) ${\displaystyle x^2+4x\sqrt{y}+4y}$=

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