-(3x%5E2-4x%2B7).jpeg "(x^2+2x-5)-(3x^2-4x+7)")
Simplifying Algebraic Expressions: (x^2 + 2x - 5) - (3x^2 - 4x + 7)
This article will guide you through the process of simplifying the algebraic expression: (x^2 + 2x - 5) - (3x^2 - 4x + 7).
Understanding the Problem
We are asked to subtract the expression (3x^2 - 4x + 7) from (x^2 + 2x - 5). This involves applying the rules of algebra to combine like terms and arrive at a simplified expression.
Step-by-Step Solution
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Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside by -1. (x^2 + 2x - 5) -1(3x^2 - 4x + 7)
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Simplify the expression: x^2 + 2x - 5 - 3x^2 + 4x - 7
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Combine like terms: Group together terms with the same variable and exponent. (x^2 - 3x^2) + (2x + 4x) + (-5 - 7)
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Simplify: -2x^2 + 6x - 12
The Solution
Therefore, the simplified expression for (x^2 + 2x - 5) - (3x^2 - 4x + 7) is -2x^2 + 6x - 12.
Key Points
- Distributing the negative sign: Remember to change the signs of all terms within the parentheses when subtracting expressions.
- Combining like terms: This is essential for simplifying algebraic expressions.
- Order of operations: Follow the order of operations (PEMDAS/BODMAS) to ensure accurate simplification.