Add. Simplify your answer. (-3x² + 2xy + 5y²) + (6x² + 8xy - y²)
Understand the Problem
The question is asking to simplify the addition of two polynomial expressions. The user needs to combine like terms in the expression (-3x² + 2xy + 5y²) + (6x² + 8xy - y²).
Answer
$$ 3x^2 + 10xy + 4y^2 $$
Answer for screen readers
$$ 3x^2 + 10xy + 4y^2 $$
Steps to Solve
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Organize the polynomial expressions First, write down the two polynomial expressions clearly: $$ (-3x^2 + 2xy + 5y^2) + (6x^2 + 8xy - y^2) $$
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Combine like terms Identify and combine the like terms from both expressions. The like terms are:
- For $x^2$: $-3x^2 + 6x^2$
- For $xy$: $2xy + 8xy$
- For $y^2$: $5y^2 - y^2$
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Perform the additions for each group of like terms
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For $x^2$: $$ -3x^2 + 6x^2 = 3x^2 $$
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For $xy$: $$ 2xy + 8xy = 10xy $$
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For $y^2$: $$ 5y^2 - y^2 = 4y^2 $$
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Write down the simplified polynomial Combine all the resulting terms: $$ 3x^2 + 10xy + 4y^2 $$
$$ 3x^2 + 10xy + 4y^2 $$
More Information
This expression is the simplified result of adding the two given polynomial expressions. Combining like terms is a fundamental concept in algebra that helps in simplifying mathematical expressions.
Tips
- Forgetting to combine all like terms or missing some terms during addition.
- Incorrectly adding the coefficients of the like terms (e.g., adding -3 and 6 incorrectly).
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