Determine weather x^2-8x+64 is a perfect square trinomial justify your answer i also need with a few more after this one

It's not a perfect square trinomial because it doesn't factor into one.
The square root of c-term 64 = 8
then the b-term coefficient would need to be -16 not -8.

x^2 - 16x + 64 = (x - 8)^2

you can also see this by calculating vertex. perfect squares have one solution which means the vertex of a perfect square trinomial is on the x-axis.

It creates dogx^2 and then flip your answer and multiply by 2