Find the product. Simplify your answer. $$ (4 z-2)(2 z+2) $$ $$ \square $$

Question

UpStudy AI · Accepted Answer

To find the product of the two binomials $$(4z - 2)$$ and $$(2z + 2)$$, follow these steps:

$$
(4z - 2)(2z + 2)
$$

**Step 1: Apply the Distributive Property (FOIL Method)**
$$
= 4z \cdot 2z + 4z \cdot 2 - 2 \cdot 2z - 2 \cdot 2
$$

**Step 2: Perform the Multiplications**
$$
= 8z^2 + 8z - 4z - 4
$$

**Step 3: Combine Like Terms**
$$
= 8z^2 + (8z - 4z) - 4
$$
$$
= 8z^2 + 4z - 4
$$

**Final Answer:**
$$
8z^2 + 4z - 4
$$
The product is $$8z^2 + 4z - 4$$.

Find the product. Simplify your answer. \[ (4 z-2)(2 z+2) \] \( \square \)