(10x^2-7x+7)-(4x^2+5x-9)

Jasonbradley

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Jun 16, 2024

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Subtracting Polynomials: A Step-by-Step Guide

In this article, we will explore how to subtract the polynomial (4x² + 5x - 9) from (10x² - 7x + 7).

Understanding the Process

Subtracting polynomials involves a few key steps:

1. Distribute the negative sign: The minus sign in front of the second polynomial applies to every term within the parentheses.
2. Combine like terms: Identify terms with the same variable and exponent and combine their coefficients.

Applying the Steps

Let's break down the subtraction:

1. Distribute the negative sign: (10x² - 7x + 7) - (4x² + 5x - 9) becomes (10x² - 7x + 7) + (-4x² - 5x + 9)

2. Combine like terms:

   • x² terms: 10x² - 4x² = 6x²
   • x terms: -7x - 5x = -12x
   • Constant terms: 7 + 9 = 16

The Result

Combining the results, we get the simplified expression: 6x² - 12x + 16.

Conclusion

Subtracting polynomials involves distributing the negative sign and combining like terms. By following these steps, we can simplify the expression and find the difference between two polynomials.