Problems often ask you to find the coefficient of a specific term in a binomial expansion. The coefficient is the number multiplying a specific power of x. For example, in the expansion

the coefficient of x2 is 1, the coefficient of x is 2, and the coefficient of x0 is 1.

To find a specifically requested coefficient, remember that each term is of the form

for some r=0…n.

For example, to find the coefficient of x4 in the expansion of (x2−x2​)8, we note that the general term is

where a is the coefficient to be determined. Focus on the powers of x, ignoring all constants:

So 16−3r=4⇒r=4. Plugging this back into the general term:

gives

(using a calculator)