Question

Determine whether the following is a trinomial square.x² - 8x + 64-O NoYes

Answer 1

A trinomial square has two possible forms:

`\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}`

So, for us to check if

`x^2-8x+64`

Is a trinomial square, we first check if the first and thrid terms are positive, because both options has positive first and thrid terms, even if a or b are negative, because they are squared in the process.

Both are positive, x² and 64.

Now, by comparison, we see that, in thi case we would have:

`\begin{gathered} a=x \\ b^2=64 \\ b=8 \end{gathered}`

If it is a trinomial square, than the middle term has to be:

`-2ab`

We use the negative form because we have a negative middle term.

So, let's see if it checks out:

`-2ab=-2x\cdot8=-16x`

We got -16x, but the middle term is -8x, they don't match.

Since they don't match, the given expression is not a trinomial square. The answer is No.