Question

Use the distributive property to find a similar expression to the algebraic expression (z + 4) (z - 4)
z^2 + 4z - 4z - 16
z^2 - 8z - 16
2z^2 - z^2 - 8
z(z) + 4z(z) - 4(4)

Answer 1

To use the distributive property for the expression \((z + 4)(z - 4)\), we will apply the FOIL method (First, Outside, Inside, Last):

1. **First:** \( z \cdot z = z^2 \)
2. **Outside:** \( z \cdot (-4) = -4z \)
3. **Inside:** \( 4 \cdot z = 4z \)
4. **Last:** \( 4 \cdot (-4) = -16 \)

Now, let's combine these results:

\[
z^2 - 4z + 4z - 16
\]

Notice that \(-4z\) and \(4z\) cancel each other out:

\[
z^2 - 16
\]

So, the simplified expression is:

\[
z^2 - 16
\]

Thus, the expression resembling the original product \((z + 4)(z - 4)\) is \(z^2 - 16\).

From your original attempt, the expression \(z^2 + 4z - 4z - 16\) simplifies to \(z^2 - 16\), but it looks like you had included an additional term that led to confusion in your intermediate options.

The other options provided do not represent the correct application of the distributive property for the expression given. The correct result using the distributive property is indeed \(z^2 - 16\).