how do I simplify (x^2+16)(x^2-16)?
I see the pattern of "difference of squares"
Did you know that (a+b)(a-b)= a^2- b^2 ?
so
(x^2 + 16)(x^2 - 16)
= x^4 - 256
thats what I thought
To simplify the expression (x^2+16)(x^2-16), you can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).
Let's apply this formula to the given expression:
(x^2+16)(x^2-16)
We can see that x^2 is common to both terms.
So, we can rewrite the expression as:
(x^2)^2 - 16^2
Now, applying the difference of squares formula, we have:
((x^2) + 16)((x^2) - 16)
Notice that we can simplify further. The first term, ((x^2) + 16), cannot be simplified any further. However, the second term, ((x^2) - 16), is another difference of squares:
((x^2) + 16)((x^2) - 16)
= ((x^2) + 16)(x + 4)(x - 4)
Therefore, the simplified form of (x^2+16)(x^2-16) is (x + 4)(x - 4)((x^2) + 16).