%E2%88%92(4x2%2B5x%E2%88%929).jpeg "(10x2−7x+7)−(4x2+5x−9)")
Simplifying the Expression: (10x²−7x+7)−(4x²+5x−9)
This article will guide you through the process of simplifying the expression (10x²−7x+7)−(4x²+5x−9).
Understanding the Problem
The expression involves subtracting two polynomials. The key to simplifying this expression is to distribute the negative sign and then combine like terms.
Step-by-Step Solution
-
Distribute the negative sign:
- The negative sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1.
- This gives us: 10x² - 7x + 7 - 4x² - 5x + 9
-
Identify and combine like terms:
- x² terms: 10x² - 4x² = 6x²
- x terms: -7x - 5x = -12x
- Constant terms: 7 + 9 = 16
-
Write the simplified expression:
- Combining all the terms, we get: 6x² - 12x + 16
Final Answer
The simplified form of the expression (10x²−7x+7)−(4x²+5x−9) is 6x² - 12x + 16.
Key Points
- Distributing the negative sign is crucial for simplifying expressions involving subtraction of polynomials.
- Combining like terms ensures the expression is in its simplest form.
By following these steps, you can confidently simplify expressions involving polynomials.