How do you factor x4 plus y4?

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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