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The image you provided contains a mathematical expression that I can help simplify and solve. Here's what I can see clearly:

The problem is:
\[
3(2x + 3)^2 - (x - 5) - (3x - 4)(x - 5)
\]

### Step-by-step solution:

1. **Expand** the squared term \((2x + 3)^2\):
   \[
   (2x + 3)^2 = (2x + 3)(2x + 3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9
   \]
   So:
   \[
   3(2x + 3)^2 = 3(4x^2 + 12x + 9) = 12x^2 + 36x + 27
   \]

2. **Expand** the product \((3x - 4)(x - 5)\) using the distributive property:
   \[
   (3x - 4)(x - 5) = 3x(x - 5) - 4(x - 5) = 3x^2 - 15x - 4x + 20 = 3x^2 - 19x + 20
   \]

3. Now we substitute these expansions into the original expression:
   \[
   12x^2 + 36x + 27 - (x - 5) - (3x^2 - 19x + 20)
   \]

4. **Distribute** the negative signs:
   \[
   12x^2 + 36x + 27 - x + 5 - 3x^2 + 19x - 20
   \]

5. **Combine like terms**:
   \[
   (12x^2 - 3x^2) + (36x + 19x - x) + (27 + 5 - 20)
   \]
   Simplifying each group:
   \[
   9x^2 + 54x + 12
   \]

### Final answer:
The simplified expression is:
\[
9x^2 + 54x + 12
\]

Would you like any further clarification or more details on any steps? Here are some related questions to expand your understanding:

1. How do you approach expanding binomials like \((a + b)^2\)?
2. Can you solve for the roots of a quadratic equation like \(9x^2 + 54x + 12 = 0\)?
3. How does distributing negative signs affect the terms in an equation?
4. How would you factor the final expression \(9x^2 + 54x + 12\)?
5. What are the applications of such algebraic expansions in real-life problems?

**Tip:** When expanding terms involving squares or products, always check for like terms that can simplify the expression!

Learn how to simplify the algebraic expression 3(2x + 3)^2 - (x - 5) - (3x - 4)(x - 5) step by step. This problem covers expanding binomials, applying the distributive property, and combining like terms. Suitable for students in Grades 9-11.

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