631° Вправа 631Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 189

631. Розкладіть на множники:

1) ${\displaystyle \sqrt{a}-2a\sqrt{a}=}$${\displaystyle \sqrt{a}\left(1-2a\right)}$;

2) ${\displaystyle 25\sqrt{x}+x\sqrt{x}=}$${\displaystyle \sqrt{x}\left(25+x\right)}$;

3) ${\displaystyle 9\sqrt{m}-n\sqrt{m}=}$${\displaystyle \sqrt{m}\left(9-n\right)}$;

4) ${\displaystyle \sqrt{x}+4y\sqrt{x}=}$${\displaystyle \sqrt{x}\left(1+4y\right)}$;

5) ${\displaystyle 6\sqrt{a}-15a\sqrt{a}=}$${\displaystyle 3\sqrt{a}\left(2-5a\right)}$;

6) ${\displaystyle 12\sqrt{n}-m\sqrt{n}-n\sqrt{n}=}$${\displaystyle \sqrt{n}\left(12-m-n\right)}$;

7) ${\displaystyle \sqrt{p}+2p\sqrt{p}-p^2\sqrt{p}=}$${\displaystyle \sqrt{p}\left(1+2p-p^2\right)}$;

8) ${\displaystyle m\sqrt{n}-mp\sqrt{n}+2mn\sqrt{n}=}$${\displaystyle m\sqrt{n}\left(1-p+2n\right)}$;

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

10) ${\displaystyle \sqrt{m}-m=}$${\displaystyle \sqrt{m}-\sqrt{m}\cdot \sqrt{m}=}$${\displaystyle \sqrt{m}\left(1-\sqrt{m}\right)}$;

11) ${\displaystyle n\sqrt{m}-m\sqrt{n}=}$${\displaystyle \sqrt{n}\cdot \sqrt{n}\cdot \sqrt{m}-\sqrt{m}\cdot \sqrt{m}\cdot \sqrt{n}=}$${\displaystyle \sqrt{mn}\left(\sqrt{n}-\sqrt{m}\right)}$;

12) ${\displaystyle 2\sqrt{y}-y\sqrt{2x}=}$${\displaystyle 2\sqrt{y}-\sqrt{y}\cdot \sqrt{y}\cdot \sqrt{2x}=}$${\displaystyle \sqrt{y}\left(2-\sqrt{2xy}\right)}$;

13) ${\displaystyle x-25=}$${\displaystyle {\left(\sqrt{x}\right)}^2-5^2=}$${\displaystyle \left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}$;

14) ${\displaystyle x-100=}$${\displaystyle {\left(\sqrt{x}\right)}^2-{10}^2=}$${\displaystyle \left(\sqrt{x}-10\right)\left(\sqrt{x}+10\right)}$;

15) ${\displaystyle x^2-5=}$${\displaystyle x^2-{\left(\sqrt{5}\right)}^2=}$${\displaystyle \left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)}$;

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

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

18) ${\displaystyle x-30=}$${\displaystyle {\left(\sqrt{x}\right)}^2-{\left(\sqrt{30}\right)}^2=}$${\displaystyle \left(\sqrt{x}-\sqrt{30}\right)\left(\sqrt{x}+\sqrt{30}\right)}$.