Write The Following In Standard Form: 6 X 3 − 8 X 4 + 5 X + 12 X 2 − 9 6x^3 - 8x^4 + 5x + 12x^2 - 9 6 X 3 − 8 X 4 + 5 X + 12 X 2 − 9 .A. 12 X 2 + 5 X + 6 X 3 − 9 − 8 X 4 12x^2 + 5x + 6x^3 - 9 - 8x^4 12 X 2 + 5 X + 6 X 3 − 9 − 8 X 4 B. − 8 X 4 − 6 X 8 + 12 X 2 + 5 X − 9 -8x^4 - 6x^8 + 12x^2 + 5x - 9 − 8 X 4 − 6 X 8 + 12 X 2 + 5 X − 9 C. 8 X 4 + 6 X 3 + 12 X 2 + 5 X − 9 8x^4 + 6x^3 + 12x^2 + 5x - 9 8 X 4 + 6 X 3 + 12 X 2 + 5 X − 9 D. − 8 X 4 + 6 X 3 + 12 X 2 + 5 X − 9 -8x^4 + 6x^3 + 12x^2 + 5x - 9 − 8 X 4 + 6 X 3 + 12 X 2 + 5 X − 9

Understanding the Basics of Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. An algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. In this article, we will focus on simplifying algebraic expressions, which is an essential skill for any mathematics student.

The Importance of Simplifying Algebraic Expressions

Simplifying algebraic expressions is a critical skill that helps students to:

• Understand complex mathematical concepts: By simplifying algebraic expressions, students can gain a deeper understanding of complex mathematical concepts, such as equations and inequalities.
• Solve mathematical problems efficiently: Simplifying algebraic expressions can help students to solve mathematical problems more efficiently, as it reduces the complexity of the problem.
• Develop problem-solving skills: Simplifying algebraic expressions requires students to think critically and develop problem-solving skills, which are essential for success in mathematics.

Simplifying Algebraic Expressions: A Step-by-Step Guide

Simplifying algebraic expressions involves rearranging the terms in the expression to make it easier to understand and work with. Here are the steps to simplify an algebraic expression:

1. Combine like terms: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms, as they both have the variable x and the same exponent (1).
2. Rearrange the terms: Rearrange the terms in the expression to group like terms together.
3. Simplify the expression: Simplify the expression by combining like terms and rearranging the terms.

Example: Simplifying the Algebraic Expression $6x^3 - 8x^4 + 5x + 12x^2 - 9$

To simplify the algebraic expression $6x^3 - 8x^4 + 5x + 12x^2 - 9$, we need to combine like terms and rearrange the terms.

• Step 1: Combine like terms: Combine the like terms in the expression, which are $6x^3$, $12x^2$, and $5x$.
• Step 2: Rearrange the terms: Rearrange the terms in the expression to group like terms together.
• Step 3: Simplify the expression: Simplify the expression by combining like terms and rearranging the terms.

The simplified expression is:

$-8x^4 + 6x^3 + 12x^2 + 5x - 9$

Conclusion

Simplifying algebraic expressions is an essential skill for any mathematics student. By following the steps outlined in this article, students can simplify algebraic expressions and gain a deeper understanding of complex mathematical concepts. Remember to combine like terms, rearrange the terms, and simplify the expression to get the final answer.

Answer

The correct answer is:

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division.

Q: Why is it important to simplify algebraic expressions?

A: Simplifying algebraic expressions is important because it helps students to:

• Understand complex mathematical concepts: By simplifying algebraic expressions, students can gain a deeper understanding of complex mathematical concepts, such as equations and inequalities.
• Solve mathematical problems efficiently: Simplifying algebraic expressions can help students to solve mathematical problems more efficiently, as it reduces the complexity of the problem.
• Develop problem-solving skills: Simplifying algebraic expressions requires students to think critically and develop problem-solving skills, which are essential for success in mathematics.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Combine like terms: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms, as they both have the variable x and the same exponent (1).
2. Rearrange the terms: Rearrange the terms in the expression to group like terms together.
3. Simplify the expression: Simplify the expression by combining like terms and rearranging the terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms, as they both have the variable x and the same exponent (1).

Q: How do I identify like terms in an algebraic expression?

A: To identify like terms in an algebraic expression, look for terms that have the same variable and exponent. For example, in the expression 2x + 3x, the terms 2x and 3x are like terms, as they both have the variable x and the same exponent (1).

Q: Can I simplify an algebraic expression with variables of different exponents?

A: Yes, you can simplify an algebraic expression with variables of different exponents. However, you cannot combine terms with variables of different exponents. For example, in the expression 2x^2 + 3x, you cannot combine the terms 2x^2 and 3x, as they have different exponents.

Q: How do I simplify an algebraic expression with negative coefficients?

A: To simplify an algebraic expression with negative coefficients, follow the same steps as before. However, when combining like terms, make sure to combine the negative coefficients correctly. For example, in the expression -2x + 3x, the terms -2x and 3x are like terms, as they both have the variable x and the same exponent (1). When combining these terms, you get 1x, which is equal to x.

Q: Can I simplify an algebraic expression with fractions?

A: Yes, you can simplify an algebraic expression with fractions. However, you need to follow the rules of fraction arithmetic, such as multiplying the numerators and denominators of the fractions. For example, in the expression 1/2x + 1/3x, you need to find a common denominator, which is 6. Then, you can combine the fractions by adding the numerators and keeping the common denominator. The result is 5/6x.

Q: How do I simplify an algebraic expression with parentheses?

A: To simplify an algebraic expression with parentheses, follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses first.
2. Exponents: Evaluate any exponents next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

Simplifying algebraic expressions is an essential skill for any mathematics student. By following the steps outlined in this article, students can simplify algebraic expressions and gain a deeper understanding of complex mathematical concepts. Remember to combine like terms, rearrange the terms, and simplify the expression to get the final answer.