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How do you factor x4 plus y4? - Answers

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



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How do you factor x4 plus y4? - Answers

https://math.answers.com/basic-math/How_do_you_factor_x4_plus_y4

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



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https://math.answers.com/basic-math/How_do_you_factor_x4_plus_y4

How do you factor x4 plus y4? - Answers

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

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      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

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