# How do you determine whether x^2-8x+81 is a perfect square trinomial?

Aug 15, 2017

${x}^{2} - 8 x + 81$ is not a perfect square trinomial.

${x}^{2} - 18 x + 81$ is a perfect square trinomial.

#### Explanation:

If you square a binomial, there is always a pattern which emerges:

In $a {x}^{2} + b x + c$:

If $a = 1$, then in a perfect square trinomial $c = {\left(\frac{b}{2}\right)}^{2}$

Check to see if 'half of $b$', squared, is equal to $c$

In ${x}^{2} - 8 x + 81 \text{ } \rightarrow {\left(\frac{- 8}{2}\right)}^{2} = 16$

$16 \ne 81$ so it is not a perfect square trinomial.

[Compare with ${x}^{2} - 18 x + 81$, where ${\left(\frac{- 18}{2}\right)}^{2} = 81$]
This would give:

${x}^{2} - 18 x + 81 = {\left(x - 9\right)}^{2}$