Combining like terms is a fundamental skill in algebra that involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. Here’s a step-by-step guide on how to do it:
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Identify Like Terms: Like terms are terms that have the same variable(s) raised to the same power. For example, in the expression \(3x^2\) and \(5x^2\), both terms are like terms because they have the same variable \(x\) raised to the power of 2.
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Group Like Terms: You can group like terms together to make it easier to combine them. For instance, in the expression \(2x + 3y - x + 4y\), you can group the \(x\) terms together and the \(y\) terms together: \[ (2x - x) + (3y + 4y) \]
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Combine the Coefficients: Add or subtract the coefficients of like terms. Using the previous example: \[ 2x - x = 1x \quad (\text{or simply } x) \] \[ 3y + 4y = 7y \]
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Write the Simplified Expression: Combine the results of the like terms you calculated to produce the simplified expression: \[ x + 7y \]
Example
Let’s combine the like terms in the expression: \[ 4a + 3b - 2a + 5b \]
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Identify Like Terms:
- Like terms for \(a\): \(4a\) and \(-2a\)
- Like terms for \(b\): \(3b\) and \(5b\)
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Group Like Terms: \[ (4a - 2a) + (3b + 5b) \]
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Combine the Coefficients: \[ 4a - 2a = 2a \] \[ 3b + 5b = 8b \]
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Write the Simplified Expression: \[ 2a + 8b \]
By following these steps, you can effectively combine like terms and simplify algebraic expressions.
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