Will having multiple domains improve my seo?

This won't do what you hope it will do. The redirect will effectively tell Google that URL no longer exists and has moved to your new URL. Plus since the new domain also won't have any links pointing to it it won't transfer any link love over either. The only positive it will have is you can use it as a shorter and more recognizable domain name which is good for users.

And just having the keywords in the domain does not automatically rank you #1 (or even well at all) just because it matches the search term. The domain name is just one of many factors affecting how a page is ranked. It's very, very common to see pages with the exact domain of a search term not rank #1 simply because other pages have much better content.

Better content = better rankings. Make that your mantra if you want to do well in the search engines.

(BTW, if this really worked everyone would buy the domains of the keywords they want to rank well for. They don't do it because it doesn't work. If it did then the first person to buy all the domains wins. Plus it is too easy to manipulate this way. The easier it is to manipulate the less it is used in the ranking algorithm if it is even used at all).

John Conde is 100% correct in everything he said.

There are two other considerations for purchasing the extra domain.

First is it easy for people to remember the extra domain? Will they possibly type it in on a guess/hope that it is relevant. bn.com is a good example of the first and usedcards.com is a good example of the second. If that is the case and this is business site there could be value in purchasing it and doing the redirect.

Secondly, if your business is in a space where there is or will be a lot of competition purchasing the domains for redirect purposes only has a lot of value in that it removes the choices for your competition and increases the domain presence of your company.

Neither of these things will effect SERP but they present other value. The company I work for currently has over 300 domain names registered just for these reasons.

There was an article last week on SEO-Moz - Exact Match Domains. So it would seem that having a domain that matches your keyword is not negligible. It wont bring you to #1, but it helps a little bit to get there (it seems).

But it will only help you if it appears in the search results, thus you will need to move your website to the new domain. This means that you need to make your previous domain have 301 redirects to the new domain so you will not lose your PR and Google Ranking for your existing pages.

Google Webmaster Tools has a section with additional information that can help you do the website redirect without breaking your current rankings, but it is still a risky process.

In your question you wanted the other domain to redirect to yours -- it will have no effect, since the newly bought "better" domain name will not appear in Google results.

Having a better domain name, makes it bold in the results. And more people might actually remember it and come directly next time. If you have a possibility to buy usedcars.com or used-cars.com, do it - and move your website to the new domain dumping the old one.