Expansion of Binomials| Algebra| ENGG10 LE1 Problem 7

Expand the following binomial

\left(x-\frac{1}{x}\right)^5

SOLUTION:

\left(x-\frac{1}{x}\right)^5

=1\left(x\right)^5\left(-\frac{1}{x}\right)^0+5\left(x\right)^4\left(-\frac{1}{x}\right)^1+10\left(x\right)^3\left(-\frac{1}{x}\right)^2+10\left(x\right)^2\left(-\frac{1}{x}\right)^3+5\left(x\right)^1\left(-\frac{1}{x}\right)^4+1\left(x\right)^0\left(-\frac{1}{x}\right)^5

=x^5-\frac{5x^4}{x}+\frac{10x^3}{x^2}-\frac{10x^2}{x^3}+\frac{5x}{x^4}-\frac{1}{x^5}

=x^5-5x^3+10x-\frac{10}{x}+\frac{5}{x^3}-\frac{1}{x^5}

Advertisements