Let's solve this step by step.

We are asked to find the difference between two expressions:

$(x^3 + x^2 + 9x) - (3x^2 + 2x + 3)$

Step 1: Distribute the negative sign

We will subtract each term inside the second parenthesis:

$(x^3 + x^2 + 9x) - (3x^2 + 2x + 3) = x^3 + x^2 + 9x - 3x^2 - 2x - 3$

Step 2: Combine like terms

• $x^3$ (no other $x^3$ terms to combine with)
• $x^2 - 3x^2 = -2x^2$
• $9x - 2x = 7x$
• The constant term is $-3$

So, the result is:

$x^3 - 2x^2 + 7x - 3$

Now, let's match the expression to the format with blanks:

[ [\ ?\ ]x^3 + [\ -2\ ]x^2 + [\ 7\ ]x + [\ -3\ ] ]

Thus, the correct answer for the missing blanks is:

• The coefficient of $x^3$ is $1$.
• The coefficient of $x^2$ is $-2$.
• The coefficient of $x$ is $7$.
• The constant term is $-3$.

Would you like further details or have any questions?

Related questions:

1. How do you subtract polynomials in general?
2. What are like terms, and how do you identify them?
3. How can you factor the resulting polynomial $x^3 - 2x^2 + 7x - 3$?
4. How does distributing the negative sign affect each term?
5. What is the difference between subtraction and addition of polynomials?

Tip:

Always remember to distribute negative signs carefully when subtracting expressions, as missing a negative can lead to incorrect results.