How do you find the 4th term in the expansion of the binomial #(x+y)^10#?

1 Answer
May 14, 2017

Answer:

Use the Binomial Theorem: #210x^4y^6#

Explanation:

Using the Binomial Theorem, you can quickly calculate the 4th term (or any #k^("th")# term).

The Binomial Theorem states that any binomial of the form #(x+a)^v# can be expanded to
#sum_(k=0)^infty ((v),(k))x^ka^(v-k)#

In trying to find the 4th term, we let #k=4# and in the binomial #(x+y)^10#, the term #a=y# and #v=10#. This gives us

#((v),(k))x^ka^(v-k)=((10),(4))x^4y^(10-4)=(10!)/((10-4)!4!)x^4y^6#
#=(10!)/(6!4!)x^4y^6=210x^4y^6#