Answer
$1-10x+60x^2$
Work Step by Step
Our aim is to write the first three terms of Maclaurin series for the given function.
We have: $f(x)=(1+2x)^{-5}$
Consider the series for the binomial series such as: $(1+x)^k =\Sigma_{n=0}^{\infty} \dbinom{k}{n}x^n$
Now, we have:
$S=\Sigma_{n=0}^{\infty} \dbinom{-5}{n}(2x)^n\\=\dbinom{-5}{0}(2x)^0+\dbinom{-5}{1}(2x)^1+\dbinom{-5}{2}(2x)^2\\=(1)(1)-(5)(2x)+(15)(4x^2) \\=1-10x+60x^2$
