Find the Cube of the Following Binomial Expression
\[ 4-\frac{1}{3x} \]
Solution:
Using identity:
\[ (a-b)^3 = a^3-b^3-3ab(a-b) \]
\[ \left(4-\frac{1}{3x}\right)^3 \]
\[ = (4)^3 – \left(\frac{1}{3x}\right)^3 – 3(4)\left(\frac{1}{3x}\right) \left(4-\frac{1}{3x}\right) \]
\[ = 64 – \frac{1}{27x^3} – \frac{4}{x} \left(4-\frac{1}{3x}\right) \]
\[ = 64 – \frac{1}{27x^3} – \frac{16}{x} + \frac{4}{3x^2} \]