What is the coefficient of x^4 in the expansion of (x+3)^7

Start by expanding (a+b)7, using Pascal's Triangle or the binomial coefficient function to work out the coefficients:a7 + 7a6b + 21a5b2 + 35a4b3 + 35a3b4 + 21a2b5 + 7ab6 + b7 , where a=x and b=3As the question wants the coefficient of x3, we need to look for a3 . The expansion gives 35a3b4, so we must substitute values in for a and b. As stated earlier, a=3 and b=3, hence; 35a3b4 = 35 * x3 * 34 = 35 * 81 * x3 = 2835x3Therefore the coefficient of x3 is 2835

JW
Answered by Josef W. Maths tutor

7921 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The point A lies on the curve with equation y=x^0.5. The tangent to this curve at A is parallel to the line 3y-2x=1 . Find an equation of this tangent at A. [5 marks]


Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions


Differentiate y= (3x^2+2x-6)^8


If cos(x)= 1/3 and x is acute, then find tan(x).


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