How do you find the 4th term in the binomial expansion for #(x - 10z)^7#? Precalculus The Binomial Theorem Pascal's Triangle and Binomial Expansion 1 Answer bp · dani83 Aug 7, 2015 #-35000x^4 z^3# Explanation: Using the binomial expansion: # (x-10z)^7 = ""^7C_0x^7(-10z)^0 + ""^7C_1 x^6 (-10z)^1 + ""^7C_2x^5(-10z)^2 + ""^7C_3 x^4(-10z)^3 + ... # where #""^nC_r = (n!)/((n-r)!r!)# The fourth term is # ""^7C_3 x^4 (-10z)^3# =#(7xx6xx5) /(1xx2xx3) x^4 (-1000z^3)# = #-35000x^4 z^3# Answer link Related questions What is Pascal's triangle? How do I find the #n#th row of Pascal's triangle? How does Pascal's triangle relate to binomial expansion? How do I find a coefficient using Pascal's triangle? How do I use Pascal's triangle to expand #(2x + y)^4#? How do I use Pascal's triangle to expand #(3a + b)^4#? How do I use Pascal's triangle to expand #(x + 2)^5#? How do I use Pascal's triangle to expand #(x - 1)^5#? How do I use Pascal's triangle to expand a binomial? How do I use Pascal's triangle to expand the binomial #(a-b)^6#? See all questions in Pascal's Triangle and Binomial Expansion Impact of this question 4454 views around the world You can reuse this answer Creative Commons License