(𝑥 − 4𝑥^2 + 7) − 5(−5𝑥^2 + 5𝑥 − 3)

Let's simplify the expression:

\[
(𝑥 − 4𝑥^2 + 7) − 5(−5𝑥^2 + 5𝑥 − 3)
\]

### Step 1: Distribute the \(-5\) over the terms inside the second parentheses:
\[
= 𝑥 − 4𝑥^2 + 7 - 5(-5𝑥^2 + 5𝑥 − 3)
\]
\[
= 𝑥 − 4𝑥^2 + 7 + 25𝑥^2 - 25𝑥 + 15
\]

### Step 2: Combine like terms:
- For \(𝑥^2\): \(-4𝑥^2 + 25𝑥^2 = 21𝑥^2\)
- For \(x\): \(x - 25𝑥 = -24𝑥\)
- Constant terms: \(7 + 15 = 22\)

Thus, the simplified expression is:
\[
21𝑥^2 - 24𝑥 + 22
\]

Let me know if you'd like further details or have any questions!

Here are some related questions you might find useful:
1. How do you factor quadratic expressions like \(21𝑥^2 - 24𝑥 + 22\)?
2. What is the method for solving quadratic equations?
3. How do you simplify more complex algebraic expressions?
4. How does distribution affect algebraic expressions?
5. How can like terms be combined in polynomial expressions?

**Tip:** Always distribute any negative signs carefully to avoid errors when simplifying algebraic expressions.

Learn how to simplify the algebraic expression (𝑥 − 4𝑥^2 + 7) − 5(−5𝑥^2 + 5𝑥 − 3) by distributing and combining like terms. This problem covers key algebra concepts like distribution and simplification of polynomials, suitable for students in Grades 8-10.

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