Find the first three terms in the binomial expansion of (8-9x)^(2/3) in ascending powers of x

Rewrite (8-9x)^(2/3) as (8(1-(9/8)x)^(2/3)=4(1-(9/8)x)^(2/3). Now apply the C4 binomial formula in the formula booklet, so: 4(1 - ((9/8)x)^(2/3)= 4[ 1 + (2/3)*((-9/8)x) + (2/3)((-9/8)x)^2 .....]= 4[ 1 - (3/4)x + (27/32)x^2 ....]=4 - 3x + (27/8)x^2.... so the first 3 terms are 4 - 3x + (27/8)x^2

AR
Answered by Anthony R. Maths tutor

12053 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.


Differentiate y = (x^2 + 3)^2


Integrate cos^2(x)


Solve the equation |3x +4a| = 5a where a is a positive constant.


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