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

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UpStudy AI · Accepted Answer

To find the product of the binomials $$ (2y + 4)(2y - 2) $$ and simplify the expression, you can use the **FOIL (First, Outer, Inner, Last)** method. Here's a step-by-step breakdown:

1. **Multiply the First terms:**
   $$
   2y \times 2y = 4y^2
   $$

2. **Multiply the Outer terms:**
   $$
   2y \times (-2) = -4y
   $$

3. **Multiply the Inner terms:**
   $$
   4 \times 2y = 8y
   $$

4. **Multiply the Last terms:**
   $$
   4 \times (-2) = -8
   $$

5. **Combine all the products:**
   $$
   4y^2 - 4y + 8y - 8
   $$

6. **Combine like terms (the terms with $$ y $$):**
   $$
   -4y + 8y = 4y
   $$

7. **Write the final simplified expression:**
   $$
   4y^2 + 4y - 8
   $$

**Final Answer:**
$$
4y^2 + 4y - 8
$$
The product simplifies to $$ 4y^2 + 4y - 8 $$.

Find the product. Simplify your answer. \( (2 y+4)(2 y-2) \)

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