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.