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in this lesson we learn how to do a binomial expansion with a negative power for a binomial that has a first term of one which is when we have two terms inside a bracket with the first being a one we can write this as a taylor series as so we can see that the power of x increases by one each time and the coefficient changes from n n brackets n minus 1 n brackets n minus 1 brackets n minus 2 and so on while the denominator of the fraction increases from two factorial to three factorial and so on this series is only valid for x values between minus one and one when n is negative the series contains an infinite number of terms so we only find the first few terms as requested in the question here are the steps factorize if necessary to make the first term one substitute the values of n and x into the formula above simplify each term and write the values of x for which the expansion is valid for example find the first four terms of 2 plus ten x to the power of negative two we always refer t
