https://file.aiquickdraw.com/mathbot/file/1726663708858mkrn21ak.jpg

The image contains several algebraic expressions within parentheses, each separated by addition or subtraction operations. Let's solve each one step by step.

### Expression 1:
\[
(3x^2 + 2x + 4) + (2x^2 - x - 2)
\]
Combine like terms:
\[
3x^2 + 2x^2 = 5x^2, \quad 2x - x = x, \quad 4 - 2 = 2
\]
Final result:
\[
5x^2 + x + 2
\]

### Expression 2:
\[
(4x + 5y - 6) + (2x + 3y + 4)
\]
Combine like terms:
\[
4x + 2x = 6x, \quad 5y + 3y = 8y, \quad -6 + 4 = -2
\]
Final result:
\[
6x + 8y - 2
\]

### Expression 3:
\[
(2x^2 - 3x + 4) - (3x^2 + 4y - 3)
\]
Distribute the negative sign and combine like terms:
\[
2x^2 - 3x^2 = -x^2, \quad -3x + 0 = -3x, \quad 4y - 4y = 0, \quad 4 + 3 = 7
\]
Final result:
\[
-x^2 - 3x + 7
\]

### Expression 4:
\[
(5x - 2y - 6) - (3x - 4y - 8)
\]
Distribute the negative sign and combine like terms:
\[
5x - 3x = 2x, \quad -2y + 4y = 2y, \quad -6 + 8 = 2
\]
Final result:
\[
2x + 2y + 2
\]

### Expression 5:
\[
(x + 3xy + 6) - (1 - 2x) + (2xy - 3)
\]
Distribute the negative sign and combine like terms:
\[
x + 2x = 3x, \quad 3xy + 2xy = 5xy, \quad 6 - 1 - 3 = 2
\]
Final result:
\[
3x + 5xy + 2
\]

---

Would you like more detailed explanations for any step? Here are 5 questions related to these operations:

1. What is the general process for combining like terms in polynomial expressions?
2. How does distributing the negative sign affect terms in subtraction?
3. Why do the constants get added or subtracted separately from the variables?
4. What role does the degree of the terms (like \(x^2\)) play in simplifying expressions?
5. How do we handle expressions with mixed terms like \(xy\)?

**Tip:** When simplifying, always pay attention to signs when distributing terms in subtraction.

Solve the algebraic expressions by combining like terms and distributing negative signs where necessary.

Learn how to simplify polynomial expressions by combining like terms and distributing negative signs. The problem involves key algebra concepts like polynomial addition and subtraction, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation