%2B(x%5E2-9x%2B3).jpeg "(x^2-4x-10)+(x^2-9x+3)")
Simplifying the Expression: (x^2-4x-10)+(x^2-9x+3)
In algebra, we often encounter expressions involving multiple terms and variables. Simplifying these expressions makes them easier to understand and manipulate. Let's look at how to simplify the expression (x^2-4x-10)+(x^2-9x+3).
Understanding the Expression
The expression contains two sets of parentheses, each representing a polynomial. Here's a breakdown:
- (x^2 - 4x - 10): This is a trinomial with a quadratic term (x^2), a linear term (-4x), and a constant term (-10).
- (x^2 - 9x + 3): Another trinomial with a quadratic term (x^2), a linear term (-9x), and a constant term (+3).
Simplifying the Expression
To simplify, we combine like terms. Remember, like terms have the same variable and exponent.
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Identify Like Terms:
- x^2 terms: x^2 and x^2
- x terms: -4x and -9x
- Constant terms: -10 and +3
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Combine Like Terms:
- x^2 + x^2 = 2x^2
- -4x - 9x = -13x
- -10 + 3 = -7
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Write the Simplified Expression: The simplified expression is 2x^2 - 13x - 7.
Conclusion
By identifying and combining like terms, we successfully simplified the expression (x^2-4x-10)+(x^2-9x+3) to 2x^2 - 13x - 7. This simplified form allows for easier manipulation and understanding of the expression.