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Use the binomial expansion formula for (a+b)³.

April 1, 2026Mathematics

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Answer

1 + \frac{6}{x} + \frac{12}{x^2} + \frac{8}{x^3}

3 steps

Use the binomial expansion formula for $(a+b)^3$ .
The formula is $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .
In this case, $a=1$ and $b=\frac{2}{x}$ .
Substitute the values of $a$ and $b$ into the formula.
$\left(1 + \frac{2}{x}\right)^3 = (1)^3 + 3(1)^2\left(\frac{2}{x}\right) + 3(1)\left(\frac{2}{x}\right)^2 + \left(\frac{2}{x}\right)^3$
Simplify each term.
$= 1 + 3(1)\left(\frac{2}{x}\right) + 3(1)\left(\frac{4}{x^2}\right) + \left(\frac{8}{x^3}\right)$ $= 1 + \frac{6}{x} + \frac{12}{x^2} + \frac{8}{x^3}$
The expanded form is:
$1 + \frac{6}{x} + \frac{12}{x^2} + \frac{8}{x^3}$

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