Expand Using the Binomial Theorem (x-2)^17

${(x - 2)}^{17}$

Step 1

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

$\sum_{k = 0}^{17} \frac{17!}{(17 - k)! k!} \cdot {(x)}^{17 - k} \cdot {(- 2)}^{k}$

Step 2

Expand the summation.

$\frac{17!}{(17 - 0)! 0!} {(x)}^{17 - 0} \cdot {(- 2)}^{0} + \frac{17!}{(17 - 1)! 1!} {(x)}^{17 - 1} \cdot {(- 2)}^{1} + \dots + \frac{17!}{(17 - 17)! 17!} {(x)}^{17 - 17} \cdot {(- 2)}^{17}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(x)}^{17} \cdot {(- 2)}^{0} + 17 \cdot {(x)}^{16} \cdot {(- 2)}^{1} + \dots + 1 \cdot {(x)}^{0} \cdot {(- 2)}^{17}$

Step 4

Simplify the polynomial result.

$x^{17} - 34 x^{16} + 544 x^{15} - 5440 x^{14} + 38080 x^{13} - 198016 x^{12} + 792064 x^{11} - 2489344 x^{10} + 6223360 x^{9} - 12446720 x^{8} + 19914752 x^{7} - 25346048 x^{6} + 25346048 x^{5} - 19496960 x^{4} + 11141120 x^{3} - 4456448 x^{2} + 1114112 x - 131072$

Expand Using the Binomial Theorem (x-2)^17

Related Questions

Support LCMGCF.com by disabling your adblocker.