https://file.aiquickdraw.com/mathbot/file/1727319690696j6vxfdq1.jpg

The expression shown in the image is:

\[
(2z - 4) \times (6z - 2)
\]

To expand and simplify this product, you can apply the distributive property (also known as FOIL for binomials):

\[
(2z - 4) \times (6z - 2) = 2z \times 6z + 2z \times (-2) + (-4) \times 6z + (-4) \times (-2)
\]

Now, let's compute each term:

1. \( 2z \times 6z = 12z^2 \)
2. \( 2z \times (-2) = -4z \)
3. \( (-4) \times 6z = -24z \)
4. \( (-4) \times (-2) = 8 \)

Now, combine the terms:

\[
12z^2 - 4z - 24z + 8 = 12z^2 - 28z + 8
\]

So the simplified result is:

\[
12z^2 - 28z + 8
\]

Would you like further explanation on any part of this solution? 

Here are five related questions to consider:
1. How do you factor the expression \(12z^2 - 28z + 8\)?
2. What happens if you solve \(12z^2 - 28z + 8 = 0\)?
3. Can you generalize the distributive property for any binomials?
4. How would the answer change if the signs in the original expression were different?
5. How do you verify if the simplified expression is correct?

**Tip**: Always check the signs when applying the distributive property to avoid errors in expansion.

Expand and simplify the polynomial expression (2z - 4) × (6z - 2) using the distributive property. Learn how to apply the FOIL method for binomials, including combining like terms. Suitable for students in Grades 8-10.

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