We start with the given expression:

$x + 8x + 16$

Step 1: Combine Like Terms

Since $x$ and $8x$ are like terms, we add them:

$9x + 16$

Step 2: Check for a Perfect Square

A perfect square trinomial has the form:

$(a + b)^2 = a^2 + 2ab + b^2$

To express $9x + 16$ as a square of a binomial, we check if it can be written in the form $(a + b)^2$.

However, $9x + 16$ is not a quadratic expression (since the highest exponent of $x$ is 1), so it cannot be written as a square of a binomial.

If you meant rewriting a similar expression like $x^2 + 8x + 16$, we can factor it as:

$(x + 4)^2$

Would you like more clarification or another example?

Related Questions:

1. How do you identify a perfect square trinomial?
2. What is the difference between factoring and expanding a binomial square?
3. How do you complete the square for quadratic expressions?
4. What are some real-life applications of perfect square trinomials?
5. How can you check if an expression is a perfect square?

Tip:

When looking for a perfect square trinomial, ensure the first and last terms are perfect squares and that the middle term is twice the product of their square roots.