Adding and subtracting algebraic expressions involves combining like terms, which are terms that have the same variable raised to the same power. Here’s a step-by-step guide:
Adding Algebraic Expressions
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Identify Like Terms: Look for terms in the expressions that have the same base and exponent. For example, in the expression \(3x^2 + 5x^2\), both terms are like terms because they both contain \(x^2\).
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Combine Like Terms: Add the coefficients of the like terms together. Using the previous example: \[ 3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2 \]
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Rewrite the Expression: Write the new expression with the combined like terms. Include any other terms that weren't like terms.
- For instance, if you have \(2x + 3 + 4x^2 + 1\): \[ 2x + 4x^2 + (3 + 1) = 4x^2 + 2x + 4 \]
Subtracting Algebraic Expressions
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Distribute the Negative Sign: When you subtract an algebraic expression, first distribute the negative sign (or the subtraction) across the entire expression you are subtracting. For instance: \[ 5x + 3 - (2x + 1) = 5x + 3 - 2x - 1 \]
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Combine Like Terms: Just as with addition, combine the like terms.
- From the previous step: \[ (5x - 2x) + (3 - 1) = 3x + 2 \]
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Rewrite the Expression: Write the new expression clearly.
- The result is \(3x + 2\).
Examples
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Addition Example: \[ (2x + 3) + (4x - 5) = 2x + 4x + 3 - 5 = 6x - 2 \]
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Subtraction Example: \[ (3y^2 + 4y) - (2y^2 + 5y) = 3y^2 - 2y^2 + 4y - 5y = (3 - 2)y^2 + (4 - 5)y = y^2 - y \]
Summary
To add or subtract algebraic expressions:
- Combine like terms by adding or subtracting their coefficients.
- Be careful when distributing the negative sign during subtraction.
- Write your final expression neatly, ensuring all like terms are combined correctly.
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