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.

Question

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 \( \boxed{16} \).