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

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UpStudy AI · Accepted Answer

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

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

$$
   \begin{align*}
   (2b - 4)(2b - 2) &= 2b \cdot 2b + 2b \cdot (-2) + (-4) \cdot 2b + (-4) \cdot (-2) \
   &= 4b^2 - 4b - 8b + 8
   \end{align*}
   $$

2. **Combine Like Terms:**

$$
   4b^2 - 4b - 8b + 8 = 4b^2 - 12b + 8
   $$

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

You can factor out a 4 to simplify further:

$$
   4b^2 - 12b + 8 = 4(b^2 - 3b + 2)
   $$

And the quadratic $$b^2 - 3b + 2$$ can be factored as $$(b - 1)(b - 2)$$, but since the problem asks for the product in a simplified form, it's typically acceptable to leave it as:

$$
   4b^2 - 12b + 8
   $$

**Final Answer:**

$$
4b^2 - 12b + 8
$$
The product simplifies to $$4b^2 - 12b + 8$$.

Find the product. Simplify your answer. \[ (2 b-4)(2 b-2) \]

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