%2B(7x%5E2-x-9).jpeg "(2x^2-6x+5)+(7x^2-x-9)")
Simplifying Polynomial Expressions: (2x^2-6x+5)+(7x^2-x-9)
In algebra, simplifying expressions is a fundamental skill. This involves combining like terms to create a more concise and manageable form. Let's examine the expression (2x^2-6x+5)+(7x^2-x-9) and break down the process of simplification.
Understanding the Problem
The expression we are given involves two polynomials:
- (2x^2-6x+5)
- (7x^2-x-9)
These polynomials are enclosed in parentheses and separated by a plus sign, indicating that we need to add them together.
Combining Like Terms
To simplify, we need to identify like terms. Like terms are terms that have the same variable raised to the same power. For example, 2x^2 and 7x^2 are like terms, while 2x^2 and 6x are not.
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Identify the like terms:
- x^2 terms: 2x^2 and 7x^2
- x terms: -6x and -x
- Constant terms: 5 and -9
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Combine the coefficients of the like terms:
- x^2 terms: 2x^2 + 7x^2 = 9x^2
- x terms: -6x - x = -7x
- Constant terms: 5 - 9 = -4
The Simplified Expression
By combining the like terms, we arrive at the simplified expression:
9x^2 - 7x - 4
This is the most concise form of the given polynomial expression.