Expand Using the Binomial Theorem (8v+s)^5

${(8 v + s)}^{5}$

Step 1

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

$\sum_{k = 0}^{5} \frac{5!}{(5 - k)! k!} \cdot {(8 v)}^{5 - k} \cdot {(s)}^{k}$

Step 2

Expand the summation.

$\frac{5!}{(5 - 0)! 0!} \cdot {(8 v)}^{5 - 0} \cdot {(s)}^{0} + \frac{5!}{(5 - 1)! 1!} \cdot {(8 v)}^{5 - 1} \cdot {(s)}^{1} + \dots + \frac{5!}{(5 - 5)! 5!} \cdot {(8 v)}^{5 - 5} \cdot {(s)}^{5}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(8 v)}^{5} \cdot {(s)}^{0} + 5 \cdot {(8 v)}^{4} \cdot {(s)}^{1} + \dots + 1 \cdot {(8 v)}^{0} \cdot {(s)}^{5}$

Step 4

Simplify the polynomial result.

$32768 v^{5} + 20480 v^{4} s + 5120 v^{3} s^{2} + 640 v^{2} s^{3} + 40 v s^{4} + s^{5}$

Expand Using the Binomial Theorem (8v+s)^5

Related Questions

Support LCMGCF.com by disabling your adblocker.