The first step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable and the same exponent — can be combined. Let's simplify the expression first.
7x^4 + 3x^3 - 5x + 1 - x^3 - 8x^2 + 5x + 3
In this case, we have one x^4-term, two x^3-terms, one x^2-term, two x-terms, and two constants. The x^3-terms, x-terms, and constants can be combined, so to simplify the expression we will rearrange them according to the Commutative Property of Addition and then combine like terms.