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Simplifying Polynomial Expressions: (x^2-4x+3)+(3x^2-3x-5)
This article will guide you through the process of simplifying the expression (x^2-4x+3)+(3x^2-3x-5).
Understanding the Problem
We have two polynomial expressions:
- x^2 - 4x + 3
- 3x^2 - 3x - 5
We are asked to add these two expressions together.
Combining Like Terms
To simplify the expression, we need to combine the like terms. Like terms are those that have the same variable and the same exponent.
1. Identify Like Terms:
- x^2 terms: x^2 and 3x^2
- x terms: -4x and -3x
- Constant terms: 3 and -5
2. Combine Like Terms:
- x^2 terms: x^2 + 3x^2 = 4x^2
- x terms: -4x - 3x = -7x
- Constant terms: 3 - 5 = -2
3. Write the Simplified Expression:
By combining the like terms, we get the simplified expression: 4x^2 - 7x - 2
Conclusion
Therefore, the simplified form of the expression (x^2-4x+3)+(3x^2-3x-5) is 4x^2 - 7x - 2.