Simplifying the Expression: (x^24x10)+(x^29x+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^24x10)+(x^29x+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.

Identify Like Terms:
 x^2 terms: x^2 and x^2
 x terms: 4x and 9x
 Constant terms: 10 and +3

Combine Like Terms:
 x^2 + x^2 = 2x^2
 4x  9x = 13x
 10 + 3 = 7

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^24x10)+(x^29x+3) to 2x^2  13x  7. This simplified form allows for easier manipulation and understanding of the expression.