Question

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

Answer 1

To use the distributive property (also known as the FOIL method for binomials) on the expression \((z + 4)(z - 4)\), we can expand it as follows:

1. **First**: Multiply the first terms: \(z \cdot z = z^2\)
2. **Outer**: Multiply the outer terms: \(z \cdot (-4) = -4z\)
3. **Inner**: Multiply the inner terms: \(4 \cdot z = 4z\)
4. **Last**: Multiply the last terms: \(4 \cdot (-4) = -16\)

Now combine the results:

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

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

\[
z^2 - 16
\]

Thus, the expression \((z + 4)(z - 4)\) simplifies to:

\[
z^2 - 16
\]

This is a difference of squares. The similar expression to \((z + 4)(z - 4)\) is:

\[
z^2 - 16
\]