How do you factor 9x^2+4y^29x2+4y2?

1 Answer
May 31, 2017

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^29x2+4y2as (3x)^2+(2y)^2(3x)2+(2y)2.
Given the formula a^2+b^2+2ab=(a+b)^2a2+b2+2ab=(a+b)2 with a=3xa=3x and b=2yb=2y you have 2ab=(2*3*2)xy=12xy2ab=(232)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=(3x)2+(2y)2+12xy12xy=[(3x)2+(2y)2+12xy]12xy=(3x+2y)212xy
This is not really a smart move in this case but i think it's the only operatio you can do with this polinom.