Write down the first three terms in the expansion, in descending powers of x, of [ax-(b/x^3)]^8. Hence evaluate the term independent of x of [5x-(1/x^3)]^8.
I dunno how to do the Hence part, making use of the terms in the expansion.
In this expansion we have terms of form:
To have a term independent of we require that the in numerator cancels out the in denominator. The exponent of in numberator is and the exponent of in denominator is . We want that so that they cancel out. Therefore, if we solve this equation.
Therefore the indepentent term is: