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

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UpStudy AI · Accepted Answer

To find the product of the binomials $$(4y - 1)(2y - 4)$$ and simplify the expression, follow these steps:

1. **Apply the Distributive Property (FOIL Method):**
   
   Multiply each term in the first binomial by each term in the second binomial:

$$
   \begin{align*}
   (4y - 1)(2y - 4) &= 4y \cdot 2y + 4y \cdot (-4) + (-1) \cdot 2y + (-1) \cdot (-4) \
   &= 8y^2 - 16y - 2y + 4
   \end{align*}
   $$

2. **Combine Like Terms:**

Combine the terms that have the same degree of $$ y $$:

$$
   8y^2 - 16y - 2y + 4 = 8y^2 - 18y + 4
   $$

3. **Check for Further Simplification:**

The quadratic expression $$ 8y^2 - 18y + 4 $$ does not factor neatly with integer coefficients, so it is already in its simplest form.

**Final Answer:**

$$
8y^2 - 18y + 4
$$
$$ 8y^2 - 18y + 4 $$

Find the product. Simplify your answer. \( (4 y-1)(2 y-4) \)

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