Expand the expression to a polynomial in standard form:
left parenthesis, 2, x, minus, 7, right parenthesis, left parenthesis, 2, x, squared, plus, 2, x, minus, 1, right parenthesis
(2x−7)(2x 
2
 +2x−1)

Let's go step by step to expand the expression \((2x - 7)(2x^2 + 2x - 1)\). We will use the distributive property (also known as the FOIL method for binomials) to distribute each term in the first parenthesis to every term in the second parenthesis.

### Step 1: Expand using Distribution
\[
(2x - 7)(2x^2 + 2x - 1)
\]
Distribute both \(2x\) and \(-7\) across the second expression:

\[
2x(2x^2 + 2x - 1) - 7(2x^2 + 2x - 1)
\]

### Step 2: Simplify Each Product
First, distribute \(2x\):
\[
2x \cdot 2x^2 + 2x \cdot 2x + 2x \cdot (-1) = 4x^3 + 4x^2 - 2x
\]

Now, distribute \(-7\):
\[
-7 \cdot 2x^2 + (-7) \cdot 2x + (-7) \cdot (-1) = -14x^2 - 14x + 7
\]

### Step 3: Combine Like Terms
Now, add all the terms together:
\[
4x^3 + 4x^2 - 2x - 14x^2 - 14x + 7
\]

Combine the \(x^2\)-terms and \(x\)-terms:
\[
4x^3 + (4x^2 - 14x^2) + (-2x - 14x) + 7
\]
\[
4x^3 - 10x^2 - 16x + 7
\]

### Final Answer (Polynomial in Standard Form)
\[
4x^3 - 10x^2 - 16x + 7
\]

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Do you have any questions or need further explanation?

Here are five related questions you could explore:
1. How do you factor polynomials like \(4x^3 - 10x^2 - 16x + 7\)?
2. How do you determine the degree of a polynomial?
3. What is the general process for distributing terms over polynomials?
4. How do you find the roots of a cubic polynomial?
5. How would the expanded polynomial change if the original expression was \((2x + 7)(2x^2 + 2x - 1)\)?

**Tip:** When combining like terms, always group powers of \(x\) systematically to avoid mistakes.

Expand the expression to a polynomial in standard form: (2x - 7)(2x^2 + 2x - 1)

Learn how to expand and simplify the polynomial expression (2x - 7)(2x^2 + 2x - 1) step by step. This solution demonstrates the use of the distributive property and how to combine like terms, suitable for students in Grades 9-11.

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