Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the following polynomial expression:
(3x^3 + 5x^2 + 10x + 4)  (x^3 + 7x^2  3x + 1)
Understanding the Steps
To simplify this expression, we'll follow these steps:

Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside that set by 1.

Combine like terms: Identify terms with the same variable and exponent, and add their coefficients.
Simplifying the Expression
Let's apply these steps to our expression:

Distributing the negative sign:
(3x^3 + 5x^2 + 10x + 4) 1(x^3 + 7x^2  3x + 1)
= 3x^3 + 5x^2 + 10x + 4 x^3  7x^2 + 3x  1

Combining like terms:
3x^3  x^3 + 5x^2  7x^2 + 10x + 3x + 4  1
= 4x^3  2x^2 + 13x + 3
Conclusion
Therefore, the simplified form of the expression (3x^3 + 5x^2 + 10x + 4)  (x^3 + 7x^2  3x + 1) is 4x^3  2x^2 + 13x + 3.