Add. Simplify your answer. (4a² - 3ab + b²) + (-2a² + 6ab + 8b²)
Understand the Problem
The question is asking to perform addition and simplification of two polynomial expressions: (4a² - 3ab + b²) + (-2a² + 6ab + 8b²). The goal is to combine like terms to arrive at a simplified form.
Answer
The simplified expression is \( 2a^2 + 3ab + 9b^2 \).
Answer for screen readers
The simplified expression is ( 2a^2 + 3ab + 9b^2 ).
Steps to Solve
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Write down the expressions to add
We start with the two polynomial expressions:
$$(4a^2 - 3ab + b^2) + (-2a^2 + 6ab + 8b^2)$$ -
Remove the parentheses
When adding, we can remove the parentheses:
$$4a^2 - 3ab + b^2 - 2a^2 + 6ab + 8b^2$$ -
Combine like terms
Now we will group and combine the like terms:
- For $a^2$: $4a^2 - 2a^2 = 2a^2$
- For $ab$: $-3ab + 6ab = 3ab$
- For $b^2$: $b^2 + 8b^2 = 9b^2$
- Write the simplified expression
Putting it all together, the combined expression is:
$$2a^2 + 3ab + 9b^2$$
The simplified expression is ( 2a^2 + 3ab + 9b^2 ).
More Information
This polynomial combines terms that share the same variables and degrees. The process of combining like terms is fundamental in algebra, aiding in simplifying expressions for easier management and understanding.
Tips
- Confusing the signs of terms when distributing them. Always pay close attention to negative signs.
- Forgetting to combine all like terms, which can lead to incomplete simplification.
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