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)
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)
16a^4 - 81b^4 =