(7x^3+2x^2-x-4)-(4x^3-3x^2+8)

2 min read Jun 16, 2024

Subtracting Polynomials: A Step-by-Step Guide

This article will guide you through the process of subtracting the polynomials (7x^3 + 2x^2 - x - 4) and (4x^3 - 3x^2 + 8). We'll break down the steps to ensure you understand the concepts involved.

Understanding Polynomial Subtraction

Subtracting polynomials involves combining like terms with careful attention to signs. Here's the key concept:

Distribute the negative sign: Before combining terms, distribute the negative sign in front of the second polynomial to every term inside the parentheses.

Step-by-Step Solution

Rewrite the expression:

(7x^3 + 2x^2 - x - 4) - (4x^3 - 3x^2 + 8)
Distribute the negative sign:

(7x^3 + 2x^2 - x - 4) + (-4x^3 + 3x^2 - 8)
Combine like terms:

(7x^3 - 4x^3) + (2x^2 + 3x^2) - x + (-4 - 8)
Simplify:

3x^3 + 5x^2 - x - 12

Final Answer

The result of subtracting the two polynomials is 3x^3 + 5x^2 - x - 12.

Key Points to Remember

Like terms: Terms with the same variable and exponent can be combined.
Sign changes: Distributing the negative sign is crucial to ensure accurate subtraction.
Order of operations: Follow the standard order of operations when simplifying.

By understanding these concepts and following the steps outlined above, you can confidently subtract any pair of polynomials.