Perform the operation.

left parenthesis, 4, x, squared, minus, 10, x, right parenthesis, plus, left parenthesis, 2, x, squared, plus, 5, x, minus, 5, right parenthesis

(4*x*2−10*x*)+(2*x*2+5*x*−5)

Let's perform the operation step by step for the expression:

\[
(4x^2 - 10x) + (2x^2 + 5x - 5)
\]

### Step 1: Combine like terms

1. **For \(x^2\):** 
   \[
   4x^2 + 2x^2 = 6x^2
   \]

2. **For \(x\):**
   \[
   -10x + 5x = -5x
   \]

3. **Constant terms:** 
   \[
   -5 \text{ (since there is no constant in the first expression)}
   \]

### Final expression:
\[
6x^2 - 5x - 5
\]

This is the simplified result of the operation.

Would you like more details or have any further questions?

Here are 5 related questions to explore further:
1. How do you factor the quadratic expression \(6x^2 - 5x - 5\)?
2. Can we solve \(6x^2 - 5x - 5 = 0\) using the quadratic formula?
3. How do you graph the quadratic equation \(y = 6x^2 - 5x - 5\)?
4. What are the roots of the equation \(6x^2 - 5x - 5 = 0\)?
5. How do you complete the square for the expression \(6x^2 - 5x - 5\)?

**Tip:** Always combine like terms first when simplifying expressions!

Learn how to simplify the polynomial expression (4x^2 − 10x) + (2x^2 + 5x − 5) by combining like terms. This step-by-step solution demonstrates key algebraic concepts, including combining quadratic and linear terms, suitable for students in Grades 8-10.

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