Expand Using the Binomial Theorem (1-2x)^n

${(1 - 2 x)}^{n}$

Use the binomial expansion theorem to find each term. The binomial theorem states ${(a + b)}^{n} = \sum_{k = 0}^{n} n C k \cdot (a^{n - k} b^{k})$ .

$\sum_{k = 0}^{n} \frac{n!}{(n - k)! k!} \cdot {(1)}^{n - k} \cdot {(- 2 x)}^{k}$

Expand the summation.

$\frac{n!}{(n)! 0!} \cdot 1^{n - 0} {(- 2 x)}^{0} + \frac{n!}{(n - 1)! 1!} \cdot 1^{n - 1} {(- 2 x)}^{1} + \dots + \frac{n!}{(n - k)! k!} \cdot 1^{n - k} {(- 2 x)}^{k} + \dots + \frac{n!}{(0)! n!} \cdot 1^{0} {(- 2 x)}^{n}$

Expand Using the Binomial Theorem (1-2x)^n

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