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 (also known as the FOIL method for binomials), we can expand the expression step by step.

Using the distributive property:

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

Now let's distribute each term:

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

Now, combine these two results:

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

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

\[ z^2 - 16 \]

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

\[ z^2 - 16 \]

So, the equivalent expression is \(z^2 - 16\).