Multiply. $$ \left(8 x^{2}-4 x+5\right)(5 x+1) $$

Question

UpStudy AI · Accepted Answer

We begin with the product:

$$
\left(8x^2 - 4x + 5\right)(5x + 1)
$$

**Step 1: Distribute each term in the first polynomial over the second polynomial**

Multiply $$8x^2$$ by each term in $$5x + 1$$:

$$
8x^2 \cdot 5x = 40x^3 \quad \text{and} \quad 8x^2 \cdot 1 = 8x^2
$$

Multiply $$-4x$$ by each term in $$5x + 1$$:

$$
-4x \cdot 5x = -20x^2 \quad \text{and} \quad -4x \cdot 1 = -4x
$$

Multiply $$5$$ by each term in $$5x + 1$$:

$$
5 \cdot 5x = 25x \quad \text{and} \quad 5 \cdot 1 = 5
$$

**Step 2: Combine all the obtained terms**

Gathering all results, we have:

$$
40x^3 + 8x^2 - 20x^2 - 4x + 25x + 5
$$

**Step 3: Combine like terms**

Combine the $$x^2$$ terms:

$$
8x^2 - 20x^2 = -12x^2
$$

Combine the $$x$$ terms:

$$
-4x + 25x = 21x
$$

Thus, the expression simplifies to:

$$
40x^3 - 12x^2 + 21x + 5
$$

**Final Answer:**

$$
40x^3 - 12x^2 + 21x + 5
$$
The product is $$40x^3 - 12x^2 + 21x + 5$$.

Multiply. \[ \left(8 x^{2}-4 x+5\right)(5 x+1) \]