is this the correct answer to factor it completely?
x^6 - 16x^4
x^4(x^2 - 16)
x^4(x+4)(x-4)
Looks OK!
Yes, the given answer x^4(x+4)(x-4) is correct for factoring the expression x^6 - 16x^4 completely.
To explain how to get this answer, we can use the factoring techniques for polynomials. Notice that in the expression x^6 - 16x^4, we can observe that both terms have a common factor of x^4.
So, we start by factoring out x^4 from both terms:
x^6 - 16x^4 = x^4(x^2 - 16)
Now, we have another expression inside the parentheses: x^2 - 16. This can be factored further using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
In the case of x^2 - 16, we have a^2 = x^2 and b^2 = 16, so we can rewrite it as:
x^2 - 16 = (x + 4)(x - 4)
Now, substituting back into our original expression, we have:
x^6 - 16x^4 = x^4(x^2 - 16) = x^4(x + 4)(x - 4)
Therefore, the answer is x^4(x + 4)(x - 4), which is the correct and completely factored form of x^6 - 16x^4.