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Simplifying the Expression: (y²−4y+9)−(3y²−6y−9)
This article will guide you through the process of simplifying the algebraic expression: (y²−4y+9)−(3y²−6y−9).
Understanding the Concept
The expression involves subtracting one polynomial from another. To do this, we will:
- Distribute the negative sign: The negative sign in front of the second parenthesis needs to be distributed to each term inside the parenthesis.
- Combine like terms: We will then group similar terms together and perform the necessary addition and subtraction operations.
Step-by-Step Simplification
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Distribute the negative sign: (y²−4y+9) - (3y²−6y−9) = y² - 4y + 9 -3y² + 6y + 9
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Combine like terms: (y² - 3y²) + (-4y + 6y) + (9 + 9)
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Simplify: -2y² + 2y + 18
Conclusion
Therefore, the simplified form of the expression (y²−4y+9)−(3y²−6y−9) is -2y² + 2y + 18.