https://file.aiquickdraw.com/mathbot/file/17286632363007os5oab5.jpg

The expression in the image is:

\[
(5x^2 - 12x + 4) - (x^2 - 4x)
\]

Let's simplify it step by step.

### Step 1: Distribute the negative sign
Apply the negative sign to each term inside the second parentheses:

\[
= (5x^2 - 12x + 4) - x^2 + 4x
\]

### Step 2: Combine like terms
Now, combine the terms with the same powers of \(x\).

- Combine the \(x^2\) terms: \(5x^2 - x^2 = 4x^2\)
- Combine the \(x\) terms: \(-12x + 4x = -8x\)
- The constant term remains \(4\).

Thus, the simplified expression is:

\[
4x^2 - 8x + 4
\]

This is the fully simplified version of the expression.

Would you like further details or explanations on any part of this process?

Here are 5 related questions to consider:
1. How do you solve quadratic equations like \(4x^2 - 8x + 4 = 0\)?
2. Can you factor the quadratic expression \(4x^2 - 8x + 4\)?
3. What is the vertex form of a quadratic expression, and how can you find it?
4. How do you find the roots of the quadratic equation \(4x^2 - 8x + 4 = 0\) using the quadratic formula?
5. How can you complete the square for the quadratic \(4x^2 - 8x + 4\)?

**Tip:** Always check for common factors in simplified expressions—sometimes the entire expression can be factored further!

Learn how to simplify the polynomial expression (5x^2 - 12x + 4) - (x^2 - 4x) by distributing the negative sign and combining like terms. This step-by-step solution covers key algebra concepts suitable for students in Grades 7-9.

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