Factor polynomial $$ 256w^{8}-z^{8} $$

$$ 256w^{8}-z^{8} = (16w^{4}+z^{4})(4w^{2}+z^{2})(2w+z)(2w-z) $$

Step 1 :

Rewrite $ 256w^8-z^8 $ as:

$$ \color{blue}{ 256w^8-z^8 = (16w^4)^2 - (z^4)^2 } $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = 16w^4 $ and $ II = z^4 $ , we have:

$$ 256w^8-z^8 = (16w^4)^2 - (z^4)^2 = ( 16w^4-z^4 ) ( 16w^4+z^4 ) $$

Step 2 :

Rewrite $ 16w^4-z^4 $ as:

$$ \color{blue}{ 16w^4-z^4 = (4w^2)^2 - (z^2)^2 } $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = 4w^2 $ and $ II = z^2 $ , we have:

$$ 16w^4-z^4 = (4w^2)^2 - (z^2)^2 = ( 4w^2-z^2 ) ( 4w^2+z^2 ) $$

Step 3 :

Rewrite $ 4w^2-z^2 $ as:

$$ \color{blue}{ 4w^2-z^2 = (2w)^2 - (z)^2 } $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = 2w $ and $ II = z $ , we have:

$$ 4w^2-z^2 = (2w)^2 - (z)^2 = ( 2w-z ) ( 2w+z ) $$

Polynomial Factoring Calculator