Упр.10.14 ГДЗ Мерзляк 10 класс Базовый уровень (Алгебра)
Раскройте скобки:
- 1) $$(5a^{0,4}+b^{0,2})(3a^{0,4}-4b^{0,2})$$;
- 5) $$(b^{\frac{4}{3}}-b^{-\frac{2}{3}})^2$$;
- 2) $$(m^{0,5}+n^{0,5})(m^{0,5}-n^{0,5})$$;
- 6) $$(x^{\frac{1}{6}}+2)(x^{\frac{1}{3}}-2x^{\frac{1}{6}}+4)$$;
- 3) $$(a^{\frac{1}{3}}-5b^{-\frac{1}{4}})(a^{\frac{1}{3}}+5b^{-\frac{1}{4}})$$;
- 7) $$(y^{1,5}-4y^{0,5})^2+8y^2$$;
- 4) $$(m^{\frac{1}{2}}-n^{\frac{1}{2}})^2$$;
- 8) $$(a^{\frac{1}{8}}-1)(a^{\frac{1}{4}}+1)(a^{\frac{1}{8}}+1)$$.
1) $$\left(5a^{0,4}+b^{0,2}\right)\left(3a^{0,4}-4b^{0,2}\right)=15a^{0,8}-20a^{0,4}b^{0,2}+3a^{0,4}b^{0,2}-4b^{0,4}$$
$$=15a^{0,8}-17a^{0,4}b^{0,2}-4b^{0,4}=15a^{\frac45}-17a^{\frac25}b^{\frac15}-4b^{\frac25}.$$
2) $$\left(m^{0,5}+n^{0,5}\right)\left(m^{0,5}-n^{0,5}\right)=m^{1}-n^{1}=m-n.$$
3) $$\left(a^{\frac13}-5b^{-\frac14}\right)\left(a^{\frac13}+5b^{-\frac14}\right)=a^{\frac23}-25b^{-\frac12}$$
$$=\sqrt[3]{a^2}-\frac{25}{\sqrt{b}}.$$
4) $$\left(m^{\frac12}-n^{\frac12}\right)^2=m-2\sqrt{mn}+n.$$
5) $$\left(b^{\frac43}-b^{-\frac23}\right)^2=b^{\frac83}-2b^{\frac23}+b^{-\frac43}$$
$$=\sqrt[3]{b^8}-2\sqrt[3]{b^2}+\frac{1}{\sqrt[3]{b^4}}.$$
6) $$\left(x^{\frac16}+2\right)\left(x^{\frac13}-2x^{\frac16}+4\right)=x^{\frac12}+8=\sqrt{x}+8.$$
7) $$\left(y^{1,5}-4y^{0,5}\right)^2+8y^2=y^3-8y^2+16y+8y^2=y^3+16y.$$
8) $$\left(a^{\frac18}-1\right)\left(a^{\frac14}+1\right)\left(a^{\frac18}+1\right)=\left(a^{\frac14}-1\right)\left(a^{\frac14}+1\right)=a^{\frac12}-1=\sqrt{a}-1.$$
Ответ: 1) $$15a^{\frac45}-17a^{\frac25}b^{\frac15}-4b^{\frac25}$$; 2) $$m-n$$; 3) $$\sqrt[3]{a^2}-\frac{25}{\sqrt{b}}$$; 4) $$m-2\sqrt{mn}+n$$; 5) $$\sqrt[3]{b^8}-2\sqrt[3]{b^2}+\frac{1}{\sqrt[3]{b^4}}$$; 6) $$\sqrt{x}+8$$; 7) $$y^3+16y$$; 8) $$\sqrt{a}-1$$.
