 
Write (2*x* + 1)(*x* − 3)(*x* − 2) in standard form.

To express the expression \((2x + 1)(x - 3)(x - 2)\) in standard form, we'll first expand it step by step.

### Step 1: Expand \((x - 3)(x - 2)\)

\[
(x - 3)(x - 2) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6
\]

### Step 2: Multiply \(2x + 1\) by the result from Step 1

\[
(2x + 1)(x^2 - 5x + 6)
\]

Distribute \(2x\) across \(x^2 - 5x + 6\):

\[
2x \cdot x^2 = 2x^3
\]
\[
2x \cdot (-5x) = -10x^2
\]
\[
2x \cdot 6 = 12x
\]

Now distribute \(1\) across \(x^2 - 5x + 6\):

\[
1 \cdot x^2 = x^2
\]
\[
1 \cdot (-5x) = -5x
\]
\[
1 \cdot 6 = 6
\]

### Step 3: Combine all the terms

\[
2x^3 - 10x^2 + 12x + x^2 - 5x + 6
\]

Combine like terms:

\[
2x^3 - 9x^2 + 7x + 6
\]

So, the expression in standard form is:

\[
2x^3 - 9x^2 + 7x + 6
\]

Would you like more details, or do you have any questions?

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1. How do you expand a quadratic expression in general?
2. What are the common methods to multiply polynomials?
3. Can you explain how to combine like terms?
4. What are other forms a polynomial can take besides standard form?
5. How does the degree of a polynomial relate to the number of roots it can have?

**Tip:** Always remember to combine like terms carefully to avoid errors in polynomial expressions.

Write (2*x* + 1)(*x* − 3)(*x* − 2) in standard form.

Master the expansion and simplification of the polynomial (2x + 1)(x - 3)(x - 2) into its standard form with this detailed step-by-step guide. Learn essential algebraic concepts, such as distributing and combining like terms, suitable for students in Grades 9-12.

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