To solve the expression [tex]\( x^3 + x^5 - x^7 \)[/tex], follow these steps:
1. Identify the terms in the expression: The expression contains three polynomial terms: [tex]\( x^3 \)[/tex], [tex]\( x^5 \)[/tex], and [tex]\( -x^7 \)[/tex].
2. Arrange the terms: Since the terms are already arranged in descending order of the exponents, no rearrangement is necessary. The terms are: [tex]\( x^5 \)[/tex], [tex]\( x^3 \)[/tex], and [tex]\( -x^7 \)[/tex].
3. Simplify the expression: This step typically involves combining like terms. However, in this case, there are no like terms to combine because all the terms have different exponents.
After examining the expression term by term, we see that it is already simplified to its most basic form, [tex]\( -x^7 + x^5 + x^3 \)[/tex].
Therefore, the final simplified expression is:
[tex]\[ -x^7 + x^5 + x^3 \][/tex]
This is the detailed, step-by-step solution for simplifying the given polynomial expression.
