Question

Write the first four terms in the expansion of: (x-2)^15

Answer 1

we have the expression

`(x-2)^(15)`

Applying the Binomial Theorem

Remember that

the coefficient of each term r of the expansion 0f (x+y)^n is given by C(n, r - 1).

so

For the first term, the coefficient is C(15,0) -----> 1

For the second term, the coefficient is C(15,1) -----> 14

For the third term, the coefficient is C(15,2) ----> 105

For the fourth term, the coefficient is C(15,3) ---> 455

therefore

the first three terms are

`\begin{gathered} (x-2)^(15)=(1)x^(15)+14x^(14)(-2)+105x^(13)(-2)^2 \\ (x-2)^(15)=x^(15)-28x^(14)+420x^(13) \end{gathered}`