-(5x%5E2-3x%2B2).jpeg "(8x^2+2x-6)-(5x^2-3x+2)")
Simplifying the Expression: (8x^2 + 2x - 6) - (5x^2 - 3x + 2)
This problem involves simplifying an expression by subtracting two polynomials. Let's break down the steps:
1. Distribute the Negative Sign
The negative sign in front of the second parenthesis needs to be distributed to each term inside the parenthesis.
(8x^2 + 2x - 6) - (5x^2 - 3x + 2) becomes (8x^2 + 2x - 6) - 5x^2 + 3x - 2
2. Combine Like Terms
Now, we can combine the terms that have the same variable and exponent:
- x^2 terms: 8x^2 - 5x^2 = 3x^2
- x terms: 2x + 3x = 5x
- Constant terms: -6 - 2 = -8
3. The Simplified Expression
Putting the combined terms together, the simplified expression is:
3x^2 + 5x - 8
Conclusion
By distributing the negative sign and combining like terms, we successfully simplified the expression (8x^2 + 2x - 6) - (5x^2 - 3x + 2) to 3x^2 + 5x - 8.