-(7x%5E5-8x%5E4%2B2x-11).jpeg "(5x^6-2x^4+9x^3+2x-4)-(7x^5-8x^4+2x-11)")
Simplifying Polynomial Expressions
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, 5x^6 - 2x^4 + 9x^3 + 2x - 4 and 7x^5 - 8x^4 + 2x - 11 are both polynomials.
Let's simplify the expression: (5x^6 - 2x^4 + 9x^3 + 2x - 4) - (7x^5 - 8x^4 + 2x - 11).
Step 1: Distribute the Negative Sign
The minus sign in front of the second parenthesis means we need to multiply each term inside the second parenthesis by -1.
This gives us:
5x^6 - 2x^4 + 9x^3 + 2x - 4 - 7x^5 + 8x^4 - 2x + 11
Step 2: Combine Like Terms
Now, we combine the terms with the same variable and exponent.
- x^6 terms:
5x^6 - x^5 terms:
-7x^5 - x^4 terms:
-2x^4 + 8x^4 = 6x^4 - x^3 terms:
9x^3 - x terms:
2x - 2x = 0 - Constant terms:
-4 + 11 = 7
Step 3: Final Result
Putting all the terms together, we get the simplified expression:
5x^6 - 7x^5 + 6x^4 + 9x^3 + 7
This is the simplified form of the original expression.