%2B(3x%5E2%2B6x%2B5).jpeg "(2x^2+4x+1)+(3x^2+6x+5)")
Simplifying Polynomial Expressions: (2x^2 + 4x + 1) + (3x^2 + 6x + 5)
This article will guide you through the process of simplifying the expression (2x^2 + 4x + 1) + (3x^2 + 6x + 5).
Understanding the Concept
The expression we're dealing with involves polynomials, which are algebraic expressions made up of variables and constants combined using addition, subtraction, multiplication, and non-negative integer exponents. The goal is to simplify the expression by combining like terms.
Simplifying the Expression
-
Identify Like Terms:
- x^2 terms: 2x^2 and 3x^2
- x terms: 4x and 6x
- Constant terms: 1 and 5
-
Combine Like Terms: Add the coefficients of the like terms together.
- x^2 terms: 2x^2 + 3x^2 = 5x^2
- x terms: 4x + 6x = 10x
- Constant terms: 1 + 5 = 6
-
Write the Simplified Expression: Combine the results from step 2.
- (2x^2 + 4x + 1) + (3x^2 + 6x + 5) = 5x^2 + 10x + 6
Conclusion
By applying the principles of combining like terms, we have successfully simplified the expression (2x^2 + 4x + 1) + (3x^2 + 6x + 5) to its simplest form: 5x^2 + 10x + 6. This process is fundamental in algebra and allows us to manipulate and solve complex equations effectively.