answersLogoWhite

0


Best Answer

You can't.

x4 + y4 is irreducible.

It's (x+yi^1.5)(x+yi^0.5)(x-yi^1.5)(x-yi^0.5). You use the equation x^2-y^2=(x+y)(x-y) and x^2+y^2=(x+yi)(x-yi).

*Edit This IS reducible.

X^4+Y^4=X^4+Y^4+2X^2Y^2 -2X^2Y^2 I add and minus 2X^2Y^2 so the value stays the same.

X^4+Y^4+2X^2Y^2=(X^2+Y^2)^2

So it equals to (X^2+Y^2)^2-2X^2Y^2.

Then, we factor using difference of squares.

(X^2+Y^2)^2-2X^2Y^2=(X^2+Y^2+sqrt2 XY)(X^2+Y^2-sqrt2 XY)

*Note the XY is not included in the sqrt sign

User Avatar

Wiki User

12y ago

Still curious? Ask our experts.

Chat with our AI personalities

JordanJordan
Looking for a career mentor? I've seen my fair share of shake-ups.
Chat with Jordan
EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra
DevinDevin
I've poured enough drinks to know that people don't always want advice—they just want to talk.
Chat with Devin
More answers
User Avatar

ProfBot

3w ago

To factor x^4 + y^4, we can use the formula for the sum of fourth powers: a^4 + b^4 = (a^2 + b^2)(a^2 - ab + b^2). Therefore, x^4 + y^4 can be factored as (x^2 + y^2)(x^2 - xy + y^2). This is the final factored form of x^4 + y^4.

User Avatar

(x ^ 2 + y ^ 2) ^ 2 - 2 * (x ^ 2 * y ^ 2)

User Avatar

User Avatar

Anonymous

Lvl 1
4y ago

x4+y4=(x2+y2)2+2(x2y2)

User Avatar
* -2(x^2*y^2)

Add your answer:

Earn +20 pts
Q: How do you factor x4 plus y4?
Write your answer...
Submit
Still have questions?
magnify glass
imp