632° Вправа 632Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 189

632. Розкладіть на множники:

1) ${\displaystyle 3\sqrt{x}-x\sqrt{x}=}$${\displaystyle \sqrt{x}\left(3-x\right)}$;

2) ${\displaystyle a\sqrt{a}+c\sqrt{a}=}$${\displaystyle \sqrt{a}\left(a+c\right)}$;

3) ${\displaystyle \sqrt{a}+2a=}$${\displaystyle \sqrt{a}+2\sqrt{a}\cdot \sqrt{a}=}$${\displaystyle \sqrt{a}\left(1+2\sqrt{a}\right)}$;

4) ${\displaystyle \sqrt{5a}-5a=}$${\displaystyle \sqrt{5a}-\sqrt{5a}\cdot \sqrt{5a}=}$${\displaystyle \sqrt{5a}\left(1-\sqrt{5a}\right)}$;

5) ${\displaystyle 4p\sqrt{m}-6m\sqrt{p}=}$${\displaystyle 2\sqrt{pm}\cdot 2\sqrt{p}-2\sqrt{pm}\cdot 3\sqrt{m}=}$${\displaystyle 2\sqrt{pm}\left(2\sqrt{p}-3\sqrt{m}\right)}$;

6) ${\displaystyle x-36=}$${\displaystyle {\left(\sqrt{x}\right)}^2-6^2=}$${\displaystyle \left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}$;

7) ${\displaystyle x^2-7=}$${\displaystyle x^2-{\left(\sqrt{7}\right)}^2=}$${\displaystyle \left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)}$;

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

9) ${\displaystyle x-26=}$${\displaystyle {\left(\sqrt{x}\right)}^2-{\left(\sqrt{26}\right)}^2=}$${\displaystyle \left(\sqrt{x}-\sqrt{26}\right)\left(\sqrt{x}+\sqrt{26}\right)}$;

10) ${\displaystyle x-11=}$${\displaystyle {\left(\sqrt{x}\right)}^2-{\left(\sqrt{11}\right)}^2=}$${\displaystyle \left(\sqrt{x}-\sqrt{11}\right)\left(\sqrt{x}+\sqrt{11}\right)}$.