Use the General Term where n=10, a= and b= to find if there is a term that is independent of x (i.e. x0). If there is, the “r” value will be either a 0 or a positive whole number.
Compare the x terms and equate it to x to the power of zero which is the term independent of x.
Extract the powers of x and find the value of r.
Since the value of r is a fraction, there is no term in the expansion the has the coefficient of x0 (independent of x).
Note: In any binomial expansion, the r value starts from 0 followed by 1,2,3… . When r=0, the term is 1, r=1, the term is 2, r=2 the term is 3 and so forth. We use the r value to find the position of a certain coefficient of x. But if that certain coefficient does not exist in the expansion, the r value will NOT be a whole number.
Small Group Tuition Additional Math (AMath) at Woodlands, Elementary Math (EMath) at Admiralty.