Keyword reversal
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Suppose you want a page in your website to rank for a two word phrase like "red wagon". So you create a page mywebsite.com/redwagon.html and optimize it for "red wagon". Suppose the domain name redwagon.com is taken, but the domain name wagonred.com is available. Is it possible to take advantage of the available domain name wagonred.com to improve the rank of mywebsite.com/redwagon.html?
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No, would be the short answer.
Every domain builds its own value in the SERP's. So registering that domain will involve lots of work to get it ranking.
If you do want to go for a exact match domain, I'd go for red-wagon.com in stead of wagonred.com. That way link building becomes more easy and red wagon and wagon red are two different things.
Using the new domain to help you rank on your main site will be a losing battle in the end. You can't pass a lot of link juice to your main site from your new domain. It's only 1 IP, 1 link (or only a few will count towards your rankings). So if you really want to rank for that keyword, build a niche site on the new domain.