Answers>Maths>IB>Article

Determine the coefficient of y^3 in the binomial expansion (2x-3y)^4

Using the method of binomial expansion (which I will cover in more detail) we get

(2x-3y)^4 = + 1(2x)^4(3y)^0  -  4(2x)^3(3y)^1  +  6(2x)^2(3y)^2  -  4(2x)^1(3y)^3  +  1(2x)^0(3y)^4  =

= 16x^4  -  96x^3 y  +  216x^2 y^2  -  216x y^3  +  81y^4

Note that we can get the coefficients 1, 4, 6, 4, 1  from Pascal's triangle, and since in the given example there is subtraction (2x-3y), there is a minus sign before each term that has 3y in an odd factor (^1, ^3 etc). You can simply remember to add a minus sign before every second term.

Now we see that in the term where y is in factor 3 as asked in the question (this is the term -216xy^3), the coefficient is -216. This is the answer we are looking for!

DM
Answered by Davids M. Maths tutor

11157 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

Consider the functions f and g where f(x)=3x-5 and g(x)=x-2. (a) Find the inverse function for f. (b) Given that the inverse of g is x+2, find (g-1 o f)(x).


find the inverse function of the following: f(x) = 3x-5


Find the intersection point/s of the equations x²+7x-3 and 3x+4


Find the constant term in the binomial expansion of (3x + 2/(x^2))^33


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning