Question

How do you factor `9x^2+4y^2`?

Answer 1

I think the only operation u can do with this polynome is writing it a a sum of squares and 'compleating the square'.

Explanation:

You can see `9x^2+4y^2`as `(3x)^2+(2y)^2`.
Given the formula `a^2+b^2+2ab=(a+b)^2` with `a=3x` and `b=2y` you have `2ab=(2*3*2)xy=12xy` so u can add and subtract it to have:
`=(3x)^2+(2y)^2+12xy-12xy=[(3x)^2+(2y)^2+12xy]-12xy=(3x+2y)^2-12xy`
This is not really a smart move in this case but i think it's the only operatio you can do with this polinom.