(1) Find the product. Simplify your an $$ (2 y-4)(y+4) $$

Question

UpStudy AI · Accepted Answer

To find the product of $$(2y - 4)(y + 4)$$ and simplify the expression, follow these steps:

1. **Use the Distributive Property (FOIL Method):**

$$
(2y - 4)(y + 4) = 2y \cdot y + 2y \cdot 4 - 4 \cdot y - 4 \cdot 4
$$

2. **Multiply Each Pair:**

$$
= 2y^2 + 8y - 4y - 16
$$

3. **Combine Like Terms:**

$$
= 2y^2 + (8y - 4y) - 16
$$
$$
= 2y^2 + 4y - 16
$$

4. **Factor Out the Greatest Common Factor (Optional):**

You can factor out a 2 to simplify further:

$$
= 2(y^2 + 2y - 8)
$$

However, since the question asks for the simplified product, the final answer is:

$$
\boxed{2y^{2} + 4y - 16}
$$
The product simplifies to $$2y^{2} + 4y - 16$$.

(1) Find the product. Simplify your an