Simplifying Polynomial Expressions: (3x^28x+1)(x^2+4)+(6x^3x)
This article will guide you through the process of simplifying the polynomial expression: (3x^28x+1)(x^2+4)+(6x^3x).
Understanding the Process
To simplify a polynomial expression, we need to combine like terms. Like terms are terms that have the same variable and exponent. For example, 3x^2 and x^2 are like terms, while 3x^2 and 3x are not.
StepbyStep Simplification

Distribute the Negative Sign: Begin by distributing the negative sign in front of the second set of parentheses:
(3x^2  8x + 1) + x^2  4 + (6x^3  x)

Combine Like Terms: Now, identify and combine like terms:
6x^3 + (3x^2 + x^2) + (8x  x) + (1  4)

Simplify: Combine the coefficients of each like term:
6x^3 + 4x^2  9x  3
Final Result
The simplified form of the expression (3x^28x+1)(x^2+4)+(6x^3x) is 6x^3 + 4x^2  9x  3.
Key Takeaways
 Distribute: Pay attention to negative signs and distribute them correctly.
 Combine: Identify like terms and combine their coefficients.
 Order: While not mandatory, it's common practice to arrange terms in descending order of exponents.