How do you use the Binomial theorem to expand #(4-5i)^3#? Precalculus The Binomial Theorem Pascal's Triangle and Binomial Expansion 1 Answer Binayaka C. Jul 5, 2017 #(4-5i)^3 = -236-115i# Explanation: We know #(a+b)^n= nC_0 a^n*b^0 +nC_1 a^(n-1)*b^1 + nC_2 a^(n-2)*b^2+..........+nC_n a^(n-n)*b^n# Here #a=4,b=-5i,n=3# We know, #nC_r = (n!)/(r!*(n-r)!# #:.3C_0 =1 , 3C_1 =3, 3C_2 =3,3C_3 =1 ; i^2=-1 ,i ^3 = -i # #:.(4-5i)^3 = 4^3+3*4^2*(-5i) +3*4*(-5i)^2+(-5i)^3# or #(4-5i)^3 = 64-240i+300i^2-125i^3# or #(4-5i)^3 = 64-240i-300+125i# or #(4-5i)^3 = -236-115i# [Ans] 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 2097 views around the world You can reuse this answer Creative Commons License