Question

use the distributive property to verify which expression is equivalent to (z + 4) (z - 4)?

Answer 1

To verify which expression is equivalent to \( (z + 4)(z - 4) \) using the distributive property, we can expand the expression.

Using the distributive property (also known as the FOIL method for binomials), we distribute each term of the first binomial to each term of the second binomial:

\[
(z + 4)(z - 4) = z \cdot z + z \cdot (-4) + 4 \cdot z + 4 \cdot (-4)
\]

Now, we perform the calculations step by step:

1. \( z \cdot z = z^2 \)
2. \( z \cdot (-4) = -4z \)
3. \( 4 \cdot z = 4z \)
4. \( 4 \cdot (-4) = -16 \)

Now, combine these results:

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

The \( -4z \) and \( 4z \) cancel each other out, leaving us with:

\[
z^2 - 16
\]

So, \( (z + 4)(z - 4) \) simplifies to \( z^2 - 16 \).

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

\[
\boxed{z^2 - 16}
\]