Rewrite the trinomial -x^2 + 8x - 16 as the square of a binomial or as the opposite of the square of a binomial.

Answer 1

We can start by looking at the first two terms (-x^2 + 8x) since a perfect square trinomial always has the form of (a + b)^2 = a^2 + 2ab + b^2, where a and b are constants.

We can see that there is a common factor of -x in the first two terms, so we can rewrite the trinomial as:

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

Now, we can see that we have two terms: -x and (x - 8), which we can try to rewrite in the form of (a + b)^2 or (a - b)^2.

For example, if we take -x = -1x and (x - 8) = (-1(-8)), we can rewrite the trinomial as:

-x^2 + 8x - 16 = (-1x + (-8))^2 - 16

Therefore, we can rewrite the trinomial as the square of a binomial with -1x - 8 as its factor:

-x^2 + 8x - 16 = (-1x - 8)^2.

Alternatively, we could also write:

-x^2 + 8x - 16 = -((-1x + 4)^2 - 0)

So, in this case, the trinomial can be rewritten as the opposite of the square of a binomial, which is (-1x + 4)^2 with the opposite sign.

Answer 2

WRONG AGAIN, expand the bot's answer to see that you don't get the original.

-x^2 + 8x - 16
= -(x^2 - 8x + 16)
= - (x - 4)^2