should i do seo for inner pages?

I have website with 16 products, my keywords are my product names. I would rather rank homepage for every keyword, but obviously homepage on site seo(meta, title, description) can not include all of my keywords. What is proper strategy in this case? Should i do separate link building for each keyword and it's inner product page?
I hope this makes some sense. English is not my first language.

i recommend to rank your subpages..

i usually do that when i have more than 3 keywords to rank...

It is good to backlink building to inner pages as well, not just the main page as that will increase the overal strength and authority of your whole domain

Definintely do inner pages as well as main page.

I look at my sub pages the same as I look at my main keyword. How much competition is there? Will your homepage give your sub pages enough juice to beat the competition? If not, then your going to need SEO. For the first couple months with a site, I only do SEO on my home page. Maybe a few links here and there to my sub pages, (all manual white hat links) and I see what happens. A lot of times, nothing more is needed and you will get ranked for those sub pages. Sometimes, that's not the case. If you want that subpage to rank, then your going to need additional SEO. There is honestly no black and white answer to this with any niche or keywords. Your just going to have to test. I suggest not doing a lot to subpages until you get a feel for what it's going to take to rank them. That's just my opinion and my strategy, I'm sure others have different opinions and strategies.

Yes you must do 80% of seo for inner pages to get some good quality traffic and also indexed links.
Better you do seo for inner pages you will get better quality traffic and rankings.

BlackHat Marketing said:

Yes you must do 80% of seo for inner pages to get some good quality traffic and also indexed links.
Better you do seo for inner pages you will get better quality traffic and rankings.

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What he said. It looks fishy to Google if your homepage is the only one with links. Done properly, you can rank inner pages quite well. Not only that, but inner pages give you more flexibility in terms of what content you want to put there. 1,500 words of very strong content, outbound links to relevant authority sites, maybe a video, lots of graphics to break up eye fatigue and social sharing buttons.

yes absolutely, it would look more natural. It definitely better for your site.