Instructions: Simplify the polynomial expression.8x(2x2+x−7)8𝑥(2𝑥2+𝑥−7)Answer: 16x16𝑥+8x+8𝑥−56x

1. Break Down the Problem

We need to simplify the expression $8x(2x^2 + x - 7)$. This involves distributing $8x$ across each term inside the parentheses.

2. Relevant Concepts

We will be using the distributive property, which states that $a(b + c) = ab + ac$. Here, $a = 8x$ and $b + c = 2x^2 + x - 7$.

3. Analysis and Detail

Let's distribute $8x$:

• First term: $8x \cdot 2x^2 = 16x^3$
• Second term: $8x \cdot x = 8x^2$
• Third term: $8x \cdot (-7) = -56x$

Now, we can combine the results: $8x(2x^2 + x - 7) = 16x^3 + 8x^2 - 56x$

4. Verify and Summarize

We have distributed $8x$ correctly across all the terms. The final expression is simplified and presented in standard polynomial form.

Final Answer

The simplified polynomial expression is: $16x^3 + 8x^2 - 56x$