-(-3x%5E3%2B2).jpeg "(4x^2-2x-1)-(-3x^3+2)")
Simplifying Polynomial Expressions
This article will guide you through simplifying the polynomial expression: (4x² - 2x - 1) - (-3x³ + 2).
Understanding the Expression
- Polynomial: A polynomial is an expression consisting of variables and constants combined using addition, subtraction, multiplication, and non-negative integer exponents.
- Terms: Individual parts of a polynomial separated by addition or subtraction signs. For example, in the given expression, the terms are: 4x², -2x, -1, -3x³, and 2.
Simplifying the Expression
Step 1: Distribute the negative sign
Remember that subtracting a quantity is the same as adding its opposite.
(4x² - 2x - 1) + (3x³ - 2)
Step 2: Combine like terms
Like terms have the same variable raised to the same power.
3x³ + 4x² - 2x - 1 - 2
Step 3: Simplify
Combine the constants.
3x³ + 4x² - 2x - 3
Final Answer
The simplified form of the expression (4x² - 2x - 1) - (-3x³ + 2) is 3x³ + 4x² - 2x - 3.
Key Points to Remember
- Always remember to distribute the negative sign when subtracting a polynomial.
- Combine like terms carefully to avoid errors.
- Arrange terms in descending order of their exponents for a standard form.
By following these simple steps, you can effectively simplify polynomial expressions.