Find the product. Simplify your answer. $$ (b+4)(4 b-1) $$

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To find the product of the two binomials $$(b + 4)$$ and $$(4b - 1)$$, we'll use the distributive property (also known as the FOIL method for binomials):

$$
(b + 4)(4b - 1)
$$

**Step 1: Multiply the first terms**

$$
b \times 4b = 4b^2
$$

**Step 2: Multiply the outer terms**

$$
b \times (-1) = -b
$$

**Step 3: Multiply the inner terms**

$$
4 \times 4b = 16b
$$

**Step 4: Multiply the last terms**

$$
4 \times (-1) = -4
$$

**Step 5: Combine all the products**

$$
4b^2 - b + 16b - 4
$$

**Step 6: Combine like terms**

$$
4b^2 + ( -b + 16b ) - 4 = 4b^2 + 15b - 4
$$

**Final Simplified Product:**

$$
\boxed{4b^2 + 15b - 4}
$$
The product is $$4b^2 + 15b - 4$$.

Find the product. Simplify your answer. \( (b+4)(4 b-1) \)

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