32 a) (x=y)^n has n+1 terms. So (k+t)^22 has 23 terms.
b) Every term in the expansion is of the form (this is ignoring the coefficients). So their degree is (22-i)+i=22.
c) If we ignore coefficients, we can use what we said in part b) with i=0, 1, 2, 3. This gives
33. Using the binomial expansion formula:
So, the first five terms would be .
34. Ignoring the coefficients, every term will be of the form . So, if we want the term without y, we need the exponant to be zero, thus 5i-15=0 or i=3. Now all we have to do is calculate the coefficent for i=3, which is simply .
Hope that helps.