%E2%88%92(%E2%88%923m2%2B10m%2B4)%3D.jpeg "(4m2−m+2)−(−3m2+10m+4)=")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through simplifying the algebraic expression (4m²−m+2)−(−3m²+10m+4).
Understanding the Problem
The expression involves:
- Polynomials: Expressions with multiple terms containing variables and constants.
- Subtraction: We need to subtract the second polynomial from the first.
Simplifying the Expression
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Distribute the negative sign: Remember that subtracting a polynomial is the same as adding its opposite. So, we can rewrite the expression as: (4m²−m+2) + (3m² - 10m - 4)
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Combine like terms: Identify terms with the same variable and exponent and combine their coefficients: (4m² + 3m²) + (-m - 10m) + (2 - 4)
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Simplify: Calculate the combined coefficients: 7m² - 11m - 2
Final Result
Therefore, the simplified form of the expression (4m²−m+2)−(−3m²+10m+4) is 7m² - 11m - 2.
Key Takeaways
- Distribute negative signs: Carefully handle subtractions in polynomials by distributing the negative sign.
- Combine like terms: Group terms with the same variable and exponent to simplify.
- Follow order of operations: Remember to perform operations in the correct order (parentheses, exponents, multiplication/division, addition/subtraction).
This approach demonstrates a systematic way to simplify algebraic expressions, ensuring accuracy and clarity.