-(6x%5E2-4xy%2B3).jpeg "(3x^2+2xy+7)-(6x^2-4xy+3)")
Simplifying Algebraic Expressions: (3x^2 + 2xy + 7) - (6x^2 - 4xy + 3)
This article will guide you through the process of simplifying the algebraic expression: (3x^2 + 2xy + 7) - (6x^2 - 4xy + 3).
Understanding the Problem
We are asked to subtract the second expression (6x^2 - 4xy + 3) from the first expression (3x^2 + 2xy + 7). To do this, we need to follow the rules of simplifying algebraic expressions.
Simplifying the Expression
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Distribute the negative sign: Remember that subtracting an expression is the same as adding its opposite. We can rewrite the expression as: (3x^2 + 2xy + 7) + (-6x^2 + 4xy - 3)
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Combine like terms: Identify terms with the same variables and exponents.
- x^2 terms: 3x^2 - 6x^2 = -3x^2
- xy terms: 2xy + 4xy = 6xy
- Constant terms: 7 - 3 = 4
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Write the simplified expression: Combine the simplified terms to get the final answer: -3x^2 + 6xy + 4
Conclusion
By following the steps of distributing the negative sign and combining like terms, we successfully simplified the expression (3x^2 + 2xy + 7) - (6x^2 - 4xy + 3) to -3x^2 + 6xy + 4. This process is fundamental to algebraic manipulation and solving equations.