%E2%88%92(4x2%2B5x%E2%88%929)-perform-the-operation.jpeg "(10x2−7x+7)−(4x2+5x−9) Perform The Operation")
Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the expression (10x²−7x+7)−(4x²+5x−9).
Understanding the Process
The key to simplifying this expression is understanding that subtracting a polynomial is equivalent to adding its opposite.
1. Distribute the Negative Sign:
Begin by distributing the negative sign in front of the second set of parentheses. This means multiplying each term inside the second parentheses by -1.
(10x²−7x+7)−(4x²+5x−9) = 10x²−7x+7 -4x² -5x + 9
2. Combine Like Terms:
Now, identify terms with the same variable and exponent (like terms).
- x² terms: 10x² - 4x² = 6x²
- x terms: -7x - 5x = -12x
- Constant terms: 7 + 9 = 16
3. Write the Simplified Expression:
Combine the simplified terms to obtain the final simplified expression.
6x² - 12x + 16
Therefore, the simplified form of (10x²−7x+7)−(4x²+5x−9) is 6x² - 12x + 16.