To put \(-2(x - 3)(x + 1)\) in standard form, we’ll expand it by distributing and simplifying.

### Step 1: Expand \((x - 3)(x + 1)\)
\[
(x - 3)(x + 1) = x^2 + x - 3x - 3 = x^2 - 2x - 3
\]

### Step 2: Distribute \(-2\) across each term
\[
-2(x^2 - 2x - 3) = -2x^2 + 4x + 6
\]

### Final Answer
The expression in standard form is:
\[
-2x^2 + 4x + 6
\]

Would you like more details or have any questions?

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Here are five related questions to explore further:
1. How do we identify the vertex of the quadratic function \(-2x^2 + 4x + 6\)?
2. What are the roots of the function \(-2x^2 + 4x + 6 = 0\)?
3. How does the coefficient of \(x^2\) affect the shape of the parabola?
4. How would the expression change if we factored it back?
5. How can we find the maximum or minimum value of this quadratic function?

**Tip:** When converting from factored to standard form, expanding and simplifying each step ensures accuracy.

Learn how to convert the quadratic expression -2(x-3)(x+1) to standard form with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomial expansion and the distributive property. Suitable for students in Grades 9-11.

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