Let's simplify the expression step by step.

The given expression is:
\[
11x^2 + 6 - \left[ 7(x^2 - 3) + 9 \right]
\]

### Step 1: Distribute the 7 inside the brackets
\[
7(x^2 - 3) = 7x^2 - 21
\]
So the expression becomes:
\[
11x^2 + 6 - \left( 7x^2 - 21 + 9 \right)
\]

### Step 2: Simplify inside the brackets
\[
7x^2 - 21 + 9 = 7x^2 - 12
\]
Now the expression is:
\[
11x^2 + 6 - (7x^2 - 12)
\]

### Step 3: Distribute the negative sign
\[
11x^2 + 6 - 7x^2 + 12
\]

### Step 4: Combine like terms
\[
(11x^2 - 7x^2) + (6 + 12) = 4x^2 + 18
\]

So, the simplified expression is:
\[
4x^2 + 18
\]

Would you like further details or explanations? Here are some related questions:

1. How would the expression change if you added a constant term outside the brackets?
2. Can you factor the simplified expression \(4x^2 + 18\)?
3. What would happen if the sign inside the brackets was reversed?
4. How would this expression change if you included higher powers of \(x\)?
5. Can you plot the simplified expression \(4x^2 + 18\) on a graph?

**Tip**: When simplifying expressions, always carefully distribute and combine like terms to avoid mistakes!

Learn how to simplify the polynomial expression 11x^2 + 6 - [7(x^2 - 3) + 9] step-by-step, using distributive properties and combining like terms. This algebra problem is perfect for students in Grades 7-10.

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