I have experience with combatting excessive phosphate, in the days when I was trying to get my planted tank established. The solution to my problem wasn't to reduce the amount of phosphate in my tank. The following is quite an in depth explanation. This is because I had to do a lot of research (and experimentation) to find the solution. Hopefully, if I can share some of what I found, it'll save time and effort for others. (I am not a biologist, but I am a scientist and can mostly get my head around the chemistry).
All plants, aquatic and terrestrial require 3 macro nutrients: N, K and P in the correct ratios. N is nitrogen, K is potassium and P is phosphate. Plant growth is usually limited by the nutrient/s (micro or macro) that is in least supply. It is also worth bearing in mind that in this context, light and carbon are also considered nutrients.
Phosphate is in fish food (or as a product of metabolism as
@Hampalong says, I can't remember which) in quantities greater than that required by the 'golden' ratio. Therefore fishtanks rarely have issues due to lack of phosphate: overfeeding and phosphate are usually the number one reason for algae problems. But they are not the only reason.
My tap water has particularly low nitrate levels (<5ppm), so without supplementing nitrate, I can't get anywhere near the right ratio of phosphate: nitrogen.
Estimative index fertilising is a method that intends to overdose all nutrients, including the one in lowest required quantities. But it also relies on frequent, large water changes to remove the excess of all the other nutrients before they cause other algae issues.
By looking at the type of algae that is a problem, you can identify which nutrient you have excess of and by looking a plant issues, you can start to identify which nutrients are the limiting factors of growth.
I have found this website really useful as it looks at both. (On different pages)
http://www.theplantedtank.co.uk/algae.htmI hope this helps explain a bit about aquatic plant nutrients and helps you identify the issues particular to your tank.