Áp dụng : (A + B)3 = A3 + 3A2B + 3AB2 + B3
11) \(\left(x^2+\frac{3}{xy}\right)^3=\left(x^2\right)^3+3\cdot\left(x^2\right)^2\cdot\frac{3}{xy}+3\cdot x^2\cdot\left(\frac{3}{xy}\right)^2+\left(\frac{3}{xy}\right)^3\)
\(=x^6+3\cdot x^4\cdot\frac{3}{xy}+3\cdot x^2\cdot\frac{9}{x^2y^2}+\frac{27}{x^3y^3}\)
\(=x^6+\frac{9x^4}{xy}+\frac{27\cdot x^2}{x^2y^2}+\frac{27}{x^3y^3}\)
\(=x^6+\frac{9x^3}{y}+\frac{27}{y^2}+\frac{27}{x^3y^3}\)
12) \(\left(x^2+\frac{2}{x}\right)^3=\left(x^2\right)^3+3\cdot\left(x^2\right)^2\cdot\frac{2}{x}+3\cdot x^2\cdot\left(\frac{2}{x}\right)^2+\left(\frac{2}{x}\right)^3\)
\(=x^6+3\cdot x^4\cdot\frac{2}{x}+3\cdot x^2\cdot\frac{4}{x^2}+\frac{8}{x^3}\)
\(=x^6+\frac{6\cdot x^4}{x}+\frac{12\cdot x^2}{x^2}+\frac{8}{x^3}\)
\(=x^6+6x^3+12+8x^3\)
13) \(\left(3y+\frac{x}{2}\right)^3=\left(3y\right)^3+3\cdot3y^2\cdot\frac{x}{2}+3\cdot3y+\left(\frac{x}{2}\right)^2+\left(\frac{x}{2}\right)^3\)
\(=27y^3+\frac{9y^2\cdot x}{2}+9y+\frac{x^2}{4}+\frac{x^3}{8}\)
14) \(\left(1\frac{1}{2}xy+1\right)^3=\left(\frac{3}{2}xy+1\right)^3=\left(\frac{3}{2}xy\right)^3+3\cdot\left(\frac{3}{2}xy\right)^2\cdot1+3\cdot\frac{3}{2}xy\cdot1^2+1^3\)
\(=\frac{27}{8}x^3y^3+3\cdot\frac{9}{4}x^2y^2+\frac{9}{2}xy+1\)
\(=\frac{27}{8}x^3y^3+\frac{27}{4}x^2y^2+\frac{9}{2}xy+1\)
15) \(\left(\frac{x^2}{2}+\frac{2}{y}\right)^3=\left(\frac{x^2}{2}\right)^3+3\cdot\left(\frac{x^2}{2}\right)^2\cdot\frac{2}{y}+3\cdot\frac{x^2}{2}\cdot\left(\frac{2}{y}\right)^2+\left(\frac{2}{y}\right)^3\)
\(=\frac{x^6}{8}+3\cdot\frac{x^4}{4}\cdot\frac{2}{y}+3\cdot\frac{x^2}{2}\cdot\frac{4}{y^2}+\frac{8}{y^3}\)
\(=\frac{x^6}{8}+\frac{3x^4}{2y}+\frac{6x^2}{y^2}+\frac{8}{y^3}\)
Còn 5 bài cuối áp dụng tương tự như thế :)
