Homogeneous polynomial
Okay, imagine we have some shapes like circles or rectangles. A homogeneous polynomial is like a recipe that tells us how to make new shapes by adding or multiplying the ones we already have. But this recipe only uses shapes that are all the same size.
So if we have a recipe like "take 2 circles and add 3 rectangles" that wouldn't be a homogeneous polynomial because circles and rectangles are different sizes. But a recipe like "take 2 circles and add 3 more circles" would be homogeneous because all the shapes are the same size.
This recipe can also have variables in it, like x and y. We can use these variables to change the size of the shapes we're using. But the important thing is that all the shapes we use have to be the same size.
So a homogeneous polynomial is like a special recipe that only uses shapes that are all the same size to make new shapes.
So if we have a recipe like "take 2 circles and add 3 rectangles" that wouldn't be a homogeneous polynomial because circles and rectangles are different sizes. But a recipe like "take 2 circles and add 3 more circles" would be homogeneous because all the shapes are the same size.
This recipe can also have variables in it, like x and y. We can use these variables to change the size of the shapes we're using. But the important thing is that all the shapes we use have to be the same size.
So a homogeneous polynomial is like a special recipe that only uses shapes that are all the same size to make new shapes.