Question

Factorization and quadratic form.

Answer 1

\[x^4+4y^4\]

Answer 2

Completing the square we arrive at:
\[(x^4+4y^4)=(x^4+4x^2y^2+4y^4)-4x^2y^2\]

Answer 3

Going further we arrive at:
\[(x^2+2y^2)^2-(2xy)^2\]

Answer 4

How do we proceed to further get this into quadratic form?
Seems to have 2 quadratic pieces

Answer 5

thats correct till there
now you can simply use :
\(A^2-B^2 =(A+B)(A-B)\)

Answer 6

\(A =x^2+2y^2 \\ B= 2xy\)

Answer 7

Also, a 4th degree polynomial, SHOULD have 2 quadratic factors

Answer 8

So we would now have:
\[(x^2+2y^2+2xy)(x^2+2y^2-2xy)\]

Answer 9

thats would be correct :)

Answer 10

The y squared would be considered my C?

Answer 11

where does C come from ?

Answer 12

you want to factor it further ?
Those quadratic does not have any real factors....or you want complex factors ?

Answer 13

No that is fine, thank you but if i were to factor further would the quadratic be used or would i need to further break it down?

Answer 14

If that quadratics had real factors, then yes, you can break it down to 2 linear factors each.

Answer 15

Thank you.

Answer 16

welcome ^_^