Which of the following shows 8x3y + x2 − 14z − 2 + 5y2x written in standard form? (1 point)

−14z + 8x3y + 5y2x − 2 + x2

8x3y + 5y2x + x2 − 14z − 2

8x3y + x2 + 5y2x − 14z − 2

x2 − 2 − 14z + 5y2x + 8x2y

The standard form of an algebraic expression typically arranges terms in descending order of the degrees of variables, grouping similar types together (e.g., powers of \(x\), \(y\), and constants).

For the expression \(8x^3y + x^2 − 14z − 2 + 5y^2x\), we can order the terms by the powers of \(x\) and \(y\).

Let's break this down:
- \(8x^3y\) (degree 4: \(x^3\) and \(y^1\))
- \(5y^2x\) (degree 3: \(y^2x\))
- \(x^2\) (degree 2: \(x^2\))
- \(-14z\) (degree 1: \(z\))
- \(-2\) (constant)

The correct order of the terms is:

**\(8x^3y + 5y^2x + x^2 − 14z − 2\)**

Thus, the correct answer is:

**\(8x^3y + 5y^2x + x^2 − 14z − 2\)**

Let me know if you need further explanation or have any questions!

### Related Questions:
1. What does the "degree" of a term refer to in polynomials?
2. How do you distinguish like terms in an algebraic expression?
3. Why is it important to write expressions in standard form?
4. What is the difference between variables and constants in an equation?
5. How can grouping terms in a specific order help in simplifying expressions?

**Tip:** Always arrange polynomials in descending powers to maintain standard form.

Which of the following shows 8x^3y + x^2 − 14z − 2 + 5y^2x written in standard form?

Learn how to write the polynomial expression 8x^3y + x^2 − 14z − 2 + 5y^2x in standard form by arranging terms in descending powers. This problem is ideal for students in Grades 8-10 and focuses on polynomial structure and algebraic manipulation.

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