What is the difference between the two polynomials 9x² + 8x and 2x² + 3x?

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Understanding the Difference Between Two Polynomials

When comparing two polynomials, we need to perform subtraction to find the difference between them. In this case, we are looking at:

  • Polynomial A: 9x² + 8x
  • Polynomial B: 2x² + 3x

Step-by-Step Subtraction

The difference can be calculated as:

   (9x² + 8x) - (2x² + 3x)

Distributing the Negative Sign

First, distribute the negative sign across Polynomial B:

   9x² + 8x - 2x² - 3x

Combining Like Terms

Next, combine the like terms (the x² terms and the x terms):

  • Combine the x² terms: 9x² – 2x² = 7x²
  • Combine the x terms: 8x – 3x = 5x

The Result

Putting it all together, the difference between the two polynomials is:

   7x² + 5x

In conclusion, the difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

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