Question

An algebra tile configuration. Only the Product spot is shown. 9 tiles are in the Product spot in 5 columns with 5 rows. First row: 1 + x squared, 4 + x. Below the + x squared tile are 4 +x tiles.
Which value is needed in the expression below to create a perfect square trinomial?

x2+8x+______

4
8
16
64

Answer 1

To determine the value needed to complete the expression \( x^2 + 8x + \_\_\_\_ \) into a perfect square trinomial, we can use the formula for completing the square.

Recall that a perfect square trinomial can be expressed as:

\[
(x + a)^2 = x^2 + 2ax + a^2
\]

In this case, we have:

- The \( x^2 \) term,
- The \( 8x \) term, which corresponds to \( 2ax \).

To find \( a \), we can set up the equation from the \( 8x \) term:

\[
2a = 8
\]

Now, solve for \( a \):

\[
a = \frac{8}{2} = 4
\]

Next, we need to find the value for \( a^2 \) to complete the trinomial:

\[
a^2 = 4^2 = 16
\]

Thus, the value needed in the expression \( x^2 + 8x + \_\_\_ \) to create a perfect square trinomial is **16**.

So, the answer is \( \boxed{16} \).