Determine whether each trinomial is a perfect square trinomial.
x^2-16x+64
the first and last terms sure are perfect squares, right?
so, if it works, it would have to be (x-8)^2
If you expand this, do you get your original expression ?
To determine whether a trinomial is a perfect square trinomial, we need to compare it with the general form of a perfect square trinomial, which is:
(a^2 + 2ab + b^2)
In this case, we have the trinomial x^2 - 16x + 64.
We can see that the first term, x^2, is a perfect square itself (x^2 = (x)^2). The last term, 64, is also a perfect square (64 = 8^2).
Now, to check if the middle term is twice the product of the square roots of the first and last terms, we can calculate:
(√x^2) * (√64) * 2 = (x) * (8) * 2 = 16x
Comparing this to the middle term in the trinomial, which is -16x, we can see that they are the same.
Therefore, x^2 - 16x + 64 is a perfect square trinomial because it can be written as (x - 8)^2.