The coefficient of the x^3 term in the expansion of (3x + a)^4 is 216. Find the value of a.
From the binomial theorem we know that the x^3 term in the expansion of the above expression must satisfy,
4C3 * (3x)^3 * a = 216x^3.
Hence, after multiplying out we must have,
108a * x^3 = 216x^3
and therefore the value of a must be 2.
AB
Answered by Adam B. • Further Mathematics tutor
6757 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.
A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.
GCSE or A-level Maths: How can I find the x and y intercepts of a cubic function?
In the expansion of (x-7)(3x**2+kx-3) the coefficient of x**2 is 0. i) Find the value of k ii) Find the coefficient of x. iii) write the fully expanded equation in terms of x