(-x^2+x-4)-(3x^2-8x-2)

Jasonbradley

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Jun 16, 2024

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Subtracting Polynomials: (-x^2+x-4)-(3x^2-8x-2)

This article will guide you through the process of subtracting the polynomials (-x^2+x-4) and (3x^2-8x-2).

Understanding the Problem

We are asked to subtract the polynomial (3x^2-8x-2) from (-x^2+x-4). This means we'll be combining like terms while paying attention to the signs of the coefficients.

Step-by-Step Solution

1. Rewrite the Expression: Start by rewriting the subtraction problem as addition, remembering to distribute the negative sign: (-x^2+x-4) + (-1)(3x^2-8x-2)

2. Distribute the Negative Sign: Multiply each term inside the second set of parentheses by -1: (-x^2 + x - 4) + (-3x^2 + 8x + 2)

3. Combine Like Terms: Group the terms with the same variable and exponent: (-x^2 - 3x^2) + (x + 8x) + (-4 + 2)

4. Simplify: Combine the coefficients: -4x^2 + 9x - 2

Final Result

The result of subtracting (3x^2-8x-2) from (-x^2+x-4) is -4x^2 + 9x - 2.

Key Takeaways

• Distributing the negative sign: Remember to change the sign of every term inside the parentheses when you subtract a polynomial.
• Combining like terms: Group terms with the same variable and exponent to simplify the expression.

By following these steps, you can confidently subtract any two polynomials.