Expand Using the Binomial Theorem (x-5)^7

${(x - 5)}^{7}$

Step 1

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

$\sum_{k = 0}^{7} \frac{7!}{(7 - k)! k!} \cdot {(x)}^{7 - k} \cdot {(- 5)}^{k}$

Step 2

Expand the summation.

$\frac{7!}{(7 - 0)! 0!} {(x)}^{7 - 0} \cdot {(- 5)}^{0} + \frac{7!}{(7 - 1)! 1!} {(x)}^{7 - 1} \cdot {(- 5)}^{1} + \dots + \frac{7!}{(7 - 7)! 7!} {(x)}^{7 - 7} \cdot {(- 5)}^{7}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(x)}^{7} \cdot {(- 5)}^{0} + 7 \cdot {(x)}^{6} \cdot {(- 5)}^{1} + \dots + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{7}$

Step 4

Simplify the polynomial result.

$x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125$

Expand Using the Binomial Theorem (x-5)^7

Related Questions

Support LCMGCF.com by disabling your adblocker.