-(x%5E2%2B3x-2).jpeg "(4x^2-2x+8)-(x^2+3x-2)")
Simplifying Polynomial Expressions: (4x^2-2x+8)-(x^2+3x-2)
This article will guide you through the process of simplifying the polynomial expression: (4x^2-2x+8)-(x^2+3x-2).
Understanding the Problem
We are tasked with subtracting the polynomial (x^2+3x-2) from (4x^2-2x+8). This involves combining like terms within the expression.
Step-by-Step Solution
-
Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1.
This gives us: 4x^2 - 2x + 8 - x^2 - 3x + 2
-
Combine like terms: Identify terms with the same variable and exponent. Group them together:
- x^2 terms: 4x^2 - x^2 = 3x^2
- x terms: -2x - 3x = -5x
- Constant terms: 8 + 2 = 10
-
Write the simplified expression: Combining all the simplified terms, we get: 3x^2 - 5x + 10
Conclusion
Therefore, the simplified form of the expression (4x^2-2x+8)-(x^2+3x-2) is 3x^2 - 5x + 10.
This process demonstrates how to simplify polynomial expressions by distributing and combining like terms.