Question

This can be factored. but how ?
x^4 + 2 x^2 y^2 + 9y ^4

Answer 1

@Mertsj

Answer 2

What makes you think it can be factored?

Answer 3

There are no factors of 9 whose sum is 2

Answer 4

my profesor said there is a technique for this, but not quad. formula

Answer 5

So you want the factors based on the roots?

Answer 6

he said diff of squares

Answer 7

we thought its prime. but he insisted that it can.

Answer 8

(x^2-2xy+3y^2)(x^2+2xy+3y^2)
according to wolframalpha.com

Answer 9

@amistre64 @jim_thompson5910

Answer 10

how about x ^4 + 4y ^4 ? can you show process ?

Answer 11

@Luis_Rivera

Answer 12

ok. Try this trick:

\[x^4+2x^2y^2+9y^4=x^4+6x^2y^2+9y^4-4x^2y^2=(x^2+3y^2)^2-(2xy)^2\]

Answer 13

so i would expand the ( x^2 +3y^2)^2 right ?

Answer 14

No. You would replace (x^2+3y^2 ) with a. Replace 2xy with b. Then you would factor that and after you factored it, resubstitute.