How do you use the Binomial Theorem to expand #(x + z) ^ 5 #? Precalculus The Binomial Theorem The Binomial Theorem 1 Answer Trevor Ryan. Feb 25, 2016 #=x^5+5x^4z+10x^3z^2+10x^2z^3+5xz^4+z^5# Explanation: The binomial theorem states that #(x+y)^n+sum_(r=1)^n ""^nC_rx^(n-r)y^r# #therefore (x+z)^5=sum_(r=1)^5""^5C_rx^(5-r)z^r# #=""^5C_0x^5+""^5C_1x^(5-1)z^1+""^5C_2x^(5-2)z^2+""^5C_3x^(5-3)z^3+""^5C_4x^(5-4)z^4+""^5C_5x^(5-5)z^5# #=x^5+5x^4z+10x^3z^2+10x^2z^3+5xz^4+z^5#. Answer link Related questions What is the binomial theorem? How do I use the binomial theorem to expand #(d-4b)^3#? How do I use the the binomial theorem to expand #(t + w)^4#? How do I use the the binomial theorem to expand #(v - u)^6#? How do I use the binomial theorem to find the constant term? How do you find the coefficient of x^5 in the expansion of (2x+3)(x+1)^8? How do you find the coefficient of x^6 in the expansion of #(2x+3)^10#? How do you use the binomial series to expand #f(x)=1/(sqrt(1+x^2))#? How do you use the binomial series to expand #1 / (1+x)^4#? How do you use the binomial series to expand #f(x)=(1+x)^(1/3 )#? See all questions in The Binomial Theorem Impact of this question 3519 views around the world You can reuse this answer Creative Commons License