Giải câu 3 trang 37 sách phát triển năng lực toán 9 tập 1

a, $\sqrt[3]{27a^{3}}+2a$ = $\sqrt[3]{(3a)^{3}}+2a$ = 3a + 2a = 5a

b, $\sqrt[3]{(a+2)^{3}}+\sqrt[3]{(a-3)^{3}}$ = a + 2 + a - 3 = 2a - 1

c, $\frac{a-4}{\sqrt[3]{a^{3}}-\sqrt{a}-2}$ = $\frac{a-4}{a-\sqrt{a}-2}$ = $\frac{(\sqrt{a}-2)(\sqrt{a}+2)}{(\sqrt{a}-2)(\sqrt{a}+1)}=\frac{\sqrt{a}+2}{\sqrt{a}+1}$

d, $\sqrt[3]{x^{3}+1+3x(x+1)}-\sqrt[3]{(x-1)^{3}}$ = $\sqrt[3]{(x^{3}+1)+3x(x+1)}-\sqrt[3]{(x-1)^{3}}$

= $\sqrt[3]{(x+1)(x^{2}-x+1)+3x(x+1)}-\sqrt[3]{(x-1)^{3}}$

= $\sqrt[3]{(x+1)(x^{2}+2x+1)}-\sqrt[3]{(x-1)^{3}}=\sqrt[3]{(x+1)(x+1)^{2}}-\sqrt[3]{(x-1)^{3}}$

= $\sqrt[3]{(x-1)^{3}}-\sqrt[3]{(x-1)^{3}}=0$