Expand Using the Binomial Theorem (3x-1)^10

${(3 x - 1)}^{10}$

Step 1

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

$\sum_{k = 0}^{10} \frac{10!}{(10 - k)! k!} \cdot {(3 x)}^{10 - k} \cdot {(- 1)}^{k}$

Step 2

Expand the summation.

$\frac{10!}{(10 - 0)! 0!} \cdot {(3 x)}^{10 - 0} \cdot {(- 1)}^{0} + \frac{10!}{(10 - 1)! 1!} \cdot {(3 x)}^{10 - 1} \cdot {(- 1)}^{1} + \dots + \frac{10!}{(10 - 10)! 10!} \cdot {(3 x)}^{10 - 10} \cdot {(- 1)}^{10}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(3 x)}^{10} \cdot {(- 1)}^{0} + 10 \cdot {(3 x)}^{9} \cdot {(- 1)}^{1} + \dots + 1 \cdot {(3 x)}^{0} \cdot {(- 1)}^{10}$

Step 4

Simplify the polynomial result.

$59049 x^{10} - 196830 x^{9} + 295245 x^{8} - 262440 x^{7} + 153090 x^{6} - 61236 x^{5} + 17010 x^{4} - 3240 x^{3} + 405 x^{2} - 30 x + 1$

Expand Using the Binomial Theorem (3x-1)^10

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