difference of two quads x^4 – y^4?

how to factor x^4-y^4?

and also factor 16a^4 - 81b^4 which is related

I know difference of two cubes is

x^3+y^3 = (x+y)(x^2-xy+y^2)

x^3-y^3 = (x-y)(x^2+xy+y^2)

and difference of two squares is

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

6 Answers

  • We treat it just like the difference of two squares, since (x^2)^2 = x^4.

    x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)

    But, you'll notice the final term is ALSO a difference of squares, so we repeat:


    Hope that helps!

  • For X4 processors, there are not much differences... they all have four CPU's, they only differ I guess by speed. But by experience, I'm using Intel Quad Core Q6600 2.4GHz with a 4GB RAM and it worked great! with a Windows Vista Home Basic.

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

    (16a^4 - 81b^4) = (4a^2 - 9b^2)(4a^2 + 9b^2)

    Hope that helps.

  • Same way that you do squares.



  • and the sum of two squares is:

    x^2 + y^2 = (x - yi)(x + yi)

    (x^4 - y^4)

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

    (x - y)(x + y)(x - yi)(x + yi)

    16a^4 - 81b^4

    (4a^2 - 9b^2) (4a^2 + 9b^2)

    (2a - 3b) (2a + 3b) (2a - 3bi) (2a + 3bi)

  • (x²-y²)(x²+y²) =


    16a^4 - 81b^4 =




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