Question

Write down the first four terms in the binomial series for
a). (1+3x)^(-6)
b). ∛(√(8-2x))

Answer 1

Just use the Binomial Theorem. I'll do one. You try the other, and come back with your work if you get stuck.
(8-2x)^(1/3)
= 8^(1/3) (-2x)^0 + (1/3) 8^(-2/3) (-2x)^1 + (1/3)(-2/3)/2 8^(-5/3) (-2x)^2 + (1/3)(-2/3)(-5/3)/3! 8^(-8/3) (-2x)^3 + ...
= 2 - x/6 - x^2/72 - 5x^3/2592 - ...