Expand the expression to a polynomial in standard form:
left parenthesis, minus, 2, x, plus, 7, right parenthesis, left parenthesis, x, squared, plus, 2, x, minus, 4, right parenthesis
(−2x+7)(x 
2
 +2x−4)

To expand the expression \((−2x+7)(x^2 + 2x−4)\), we use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step process:

### Step 1: Distribute \(-2x\) to each term in the second polynomial:
\[
-2x(x^2) + (-2x)(2x) + (-2x)(-4)
\]
This gives:
\[
-2x^3 - 4x^2 + 8x
\]

### Step 2: Distribute \(7\) to each term in the second polynomial:
\[
7(x^2) + 7(2x) + 7(-4)
\]
This gives:
\[
7x^2 + 14x - 28
\]

### Step 3: Combine all the terms:
\[
(-2x^3 - 4x^2 + 8x) + (7x^2 + 14x - 28)
\]

### Step 4: Simplify by combining like terms:
\[
-2x^3 + (-4x^2 + 7x^2) + (8x + 14x) - 28
\]
This simplifies to:
\[
-2x^3 + 3x^2 + 22x - 28
\]

### Final Answer:
The expanded polynomial in standard form is:
\[
-2x^3 + 3x^2 + 22x - 28
\]

Would you like further details or have any questions?

### 5 Related Questions:
1. How do you factor a cubic polynomial like \(-2x^3 + 3x^2 + 22x - 28\)?
2. How do you use the distributive property for higher-degree polynomials?
3. What is the importance of standard form in polynomial equations?
4. Can you explain how to find the roots of a cubic polynomial?
5. How would you graph the polynomial \(-2x^3 + 3x^2 + 22x - 28\)?

### Tip:
When expanding polynomials, always combine like terms carefully to ensure accuracy in your final result.

Expand the expression to a polynomial in standard form: (−2x+7)(x^2 +2x−4)

Learn how to expand and simplify the polynomial (−2x+7)(x^2 + 2x − 4) using the distributive property. This detailed solution involves key algebraic concepts such as combining like terms and expressing the result in standard form. Suitable for high school students in Grades 9-11.

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