Subtracting Polynomials: A StepbyStep 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.
StepbyStep 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.