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Simplifying Algebraic Expressions: (10x² - 7x + 7) - (4x² + 5x - 9)
This article will guide you through simplifying the given algebraic expression: (10x² - 7x + 7) - (4x² + 5x - 9)
Understanding the Problem
We have two expressions enclosed in parentheses, with a subtraction sign between them. To simplify this, we need to follow the order of operations (PEMDAS/BODMAS) and distribute the negative sign.
Simplifying the Expression
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Distribute the negative sign: This means multiplying each term inside the second set of parentheses by -1:
(10x² - 7x + 7) - (4x² + 5x - 9)
= 10x² - 7x + 7 - 4x² - 5x + 9 -
Combine like terms: Identify terms with the same variable and exponent, and add or subtract their coefficients:
10x² - 4x² - 7x - 5x + 7 + 9 = 6x² - 12x + 16
Final Result
The simplified expression is 6x² - 12x + 16.
Key Points
- Distributing the negative sign: Remember to change the sign of each term within the parentheses following the subtraction sign.
- Combining like terms: This involves adding or subtracting coefficients of terms with the same variable and exponent.
By following these steps, you can successfully simplify algebraic expressions involving parentheses and subtraction.