%2B(4x%5E3-5x%5E2%2B2x-1).jpeg "(4x^3-2x^2+6)+(4x^3-5x^2+2x-1)")
Simplifying Polynomial Expressions
In algebra, simplifying polynomial expressions often involves combining like terms. This process helps us write the expression in its most concise form. Let's take a look at the expression:
(4x^3 - 2x^2 + 6) + (4x^3 - 5x^2 + 2x - 1)
Step 1: Identify like terms
- x^3 terms: 4x^3 and 4x^3
- x^2 terms: -2x^2 and -5x^2
- x terms: 2x
- Constant terms: 6 and -1
Step 2: Combine like terms
- x^3 terms: 4x^3 + 4x^3 = 8x^3
- x^2 terms: -2x^2 - 5x^2 = -7x^2
- x terms: 2x (remains as is)
- Constant terms: 6 - 1 = 5
Step 3: Write the simplified expression
After combining like terms, the simplified expression is:
8x^3 - 7x^2 + 2x + 5
Conclusion
By systematically identifying and combining like terms, we were able to simplify the given polynomial expression. The resulting expression 8x^3 - 7x^2 + 2x + 5 is in its most concise form, making it easier to understand and work with.