Question

Rút gọn biểu thức sau:

a)M=\(3x-\sqrt[3]{27^3+27x^2+9x+1}\)

b)N=\(\sqrt[3]{8x^3+12x^2+6x+1}-\sqrt[3]{x^3}\)

Answer 1

a: Sửa đề: \(M=3x-\sqrt[3]{27x^3+27x^2+9x+1}\)

\(=3x-\sqrt[3]{\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3}\)

\(=3x-\sqrt[3]{\left(3x+1\right)^3}\)

\(=3x-3x-1=-1\)

b: \(N=\sqrt[3]{8x^3+12x^2+6x+1}-\sqrt[3]{x^3}\)

\(=\sqrt[3]{\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3}-x\)

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

=2x+1-x

=x+1