(3a^2-5ab+b^2)+(-3a^2+2b^2+8ab)

2 min read Jun 16, 2024

Simplifying Algebraic Expressions: (3a^2-5ab+b^2)+(-3a^2+2b^2+8ab)

This article will guide you through simplifying the expression (3a^2-5ab+b^2)+(-3a^2+2b^2+8ab).

Understanding the Process

Simplifying algebraic expressions involves combining like terms. Like terms are terms that have the same variables raised to the same powers. For example, 3a^2 and -3a^2 are like terms, but 3a^2 and 5ab are not.

Step-by-Step Solution

Remove the parentheses: Since we are adding the expressions, the parentheses don't affect the order of operations.
```
(3a^2 - 5ab + b^2) + (-3a^2 + 2b^2 + 8ab) = 3a^2 - 5ab + b^2 - 3a^2 + 2b^2 + 8ab 
```

Identify and group like terms:

(3a^2 - 3a^2) + (-5ab + 8ab) + (b^2 + 2b^2)

Combine like terms:
```
0 + 3ab + 3b^2
```

Final Answer

The simplified expression is 3ab + 3b^2.

Key Points to Remember

Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
Combining Like Terms: Only combine terms that have the same variables raised to the same powers.
Signs: Pay close attention to the signs of the terms when combining them.

By following these steps, you can simplify any algebraic expression effectively.