(5x^6-2x^4+9x^3+2x-4)-(7x^5-8x^4+2x-11)

2 min read Jun 16, 2024
(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.