Simplifying Polynomial Expressions
This article will guide you through simplifying the following polynomial expression:
(6x^3  9x^2  10x + 6) + (8x^4  5x^3 + 4x^2 + 9x + 3)
Understanding the Process
Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variable and exponent. For example, 3x^2 and 2x^2 are like terms because they both have the variable 'x' raised to the power of 2.
StepbyStep Solution

Remove Parentheses: Since we are adding the two polynomials, the parentheses do not change the signs of the terms inside.
(6x^3  9x^2  10x + 6) + (8x^4  5x^3 + 4x^2 + 9x + 3) = 6x^3  9x^2  10x + 6 + 8x^4  5x^3 + 4x^2 + 9x + 3

Rearrange Terms: It's helpful to rearrange the terms to group like terms together.
8x^4  6x^3  5x^3  9x^2 + 4x^2  10x + 9x + 6 + 3

Combine Like Terms: Combine the coefficients of the like terms.
8x^4  11x^3  5x^2  x + 9
Result
The simplified form of the polynomial expression is: 8x^4  11x^3  5x^2  x + 9