# 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)

• 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:

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

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.

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

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

• 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) =

(x+y)(x-y)(x²+y²)

16a^4 - 81b^4 =

(4a²+9b²)(4a²-9b²)=

(4a²+9b²)(2a+3b)(2a-3b).

.....