factor completely
256-x^4
(16-x^2) = (4-x)(4+x)
You just didn't factor it completely.
To factor the expression 256 - x^4, we can use the difference of squares formula. The difference of squares formula states that for any two numbers a and b, the expression a^2 - b^2 can be factored as (a + b)(a - b).
In the given expression, we have 256 - x^4. We can rewrite it as (16^2) - (x^2)^2. Notice that 16 is a perfect square and x^2 is also a perfect square.
Using the difference of squares formula, we can factor 256 - x^4 as follows:
(16 + x^2)(16 - x^2)
Now, we can further factor x^2 - 16 using the difference of squares formula again:
(16 + x^2)(4 + x)(4 - x)
So, the fully factored form of 256 - x^4 is (16 + x^2)(4 + x)(4 - x).
256-x^4
(16-x^2)(16+x^2)