Simplifying the Algebraic Expression: 1 + x^3/6 + 5x in Standard Form
In algebra, simplifying expressions is an essential skill to master. In this article, we will explore how to simplify the expression 1 + x^3/6 + 5x in standard form.
What is Standard Form?
In algebra, standard form refers to the simplest form of an algebraic expression, where the terms are written in descending order of powers of the variable (usually x). The standard form of an expression is useful for comparing and adding or subtracting expressions.
Breaking Down the Expression
Let's break down the given expression:
1 + x^3/6 + 5x
To simplify this expression, we need to follow the order of operations (PEMDAS):
- Divide x^3 by 6: x^3/6 = (1/6)x^3
- Combine the constant term with the simplified expression: 1 + (1/6)x^3 + 5x
The Simplified Expression in Standard Form
Now, let's arrange the terms in descending order of powers of x:
(1/6)x^3 + 5x + 1
This is the simplified expression in standard form. Notice how the terms are written in descending order of powers of x (x^3, x, and the constant term).
Conclusion
In this article, we have successfully simplified the expression 1 + x^3/6 + 5x in standard form. By following the order of operations and rearranging the terms in descending order of powers of x, we obtained the simplified expression (1/6)x^3 + 5x + 1. This skill is essential in algebra and will be useful in various mathematical applications.
