Question

Use the binomial theorem to expand the binomial. (s + 4v)^5

Answer 1

Answer:

$(s+4v)^5 = \sum\limits_{k=0}^{5} {5 \choose k} s^{5-k} (4v)^k = s^5 + 20 s^4 v + 160 s^3 v^2 + 640 s^2 v^3 + 1280 s v^4 + 1024 v^5$

Step-by-step explanation:

Remember that the binomial theorem says that

$(a+b)^n = \sum\limits_{k=0}^{n} {n \choose k} a^k b^{n-k}$

For this case   $a = s , \\b = 4v \\n = 5$

Therefore

$(s+4v)^5 = \sum\limits_{k=0}^{5} {5 \choose k} s^{5-k} (4v)^k = s^5 + 20 s^4 v + 160 s^3 v^2 + 640 s^2 v^3 + 1280 s v^4 + 1024 v^5$

Answer 2

Answer:

S^5+20s^4 v+160s^3 v^2 + 640s^2 v^3 + 1280sv^4 + 1024v^5