Simplify The Following Expression:$\[3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3\\]A. $\[7x^5 - 6x^4 + 5x^3 - X^2 + 4x\\]B. $\[7x^5 - X^3 - X^2 + 4x\\]C. $\[7x^5 + 6x^4 - X^3 - X^2 + 4x\\]D. $\[10x^4

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, using the given expression as an example. We will break down the expression into smaller parts, combine like terms, and arrive at the final simplified expression.

The Given Expression

The given expression is:

${3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3}$

Step 1: Combine Like Terms

The first step in simplifying the expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this expression, we have several like terms:

• $3x^4$ and $-3x^4$ are like terms because they both have the variable $x$ raised to the power of 4.
• $2x^3$ and $-3x^3$ are like terms because they both have the variable $x$ raised to the power of 3.
• $-5x^2$ and $4x^2$ are like terms because they both have the variable $x$ raised to the power of 2.
• $6x$ and $-2x$ are like terms because they both have the variable $x$ raised to the power of 1.

We can combine these like terms by adding or subtracting their coefficients.

Step 2: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression further.

${3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3}$

${= (3x^4 - 3x^4) + (2x^3 - 3x^3) + (-5x^2 + 4x^2) + (6x - 2x) + 7x^5}$

${= 0 + (-x^3) + (-x^2) + (4x) + 7x^5}$

${= -x^3 - x^2 + 4x + 7x^5}$

However, we can simplify it further by rearranging the terms in descending order of the exponent of $x$.

${= 7x^5 - x^3 - x^2 + 4x}$

Conclusion

In this article, we have simplified the given algebraic expression by combining like terms and rearranging the terms in descending order of the exponent of $x$. The final simplified expression is:

${7x^5 - x^3 - x^2 + 4x}$

This expression is the correct answer among the given options.

Answer

The correct answer is:

${7x^5 - x^3 - x^2 + 4x}$

This is option B.

Final Answer

Introduction

In our previous article, we explored the process of simplifying algebraic expressions using the given expression as an example. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x^2$ and $-3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. For example, $2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$.

Q: What is the order of operations for simplifying algebraic expressions?

A: The order of operations for simplifying algebraic expressions is:

1. Combine like terms.
2. Simplify any expressions inside parentheses.
3. Simplify any exponential expressions.
4. Simplify any multiplication and division expressions from left to right.
5. Simplify any addition and subtraction expressions from left to right.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you need to combine like terms for each variable. For example, if you have the expression $2x^2y + 3x^2y - 4x^2y$, you can combine the like terms for the variable $x^2y$ as follows:

${2x^2y + 3x^2y - 4x^2y = (2 + 3 - 4)x^2y = 1x^2y}$

Q: Can I simplify an expression with a negative exponent?

A: Yes, you can simplify an expression with a negative exponent. A negative exponent indicates that the variable is in the denominator of a fraction. For example, if you have the expression $x^{-2}$, you can simplify it as follows:

${x^{-2} = \frac{1}{x^2}}$

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you need to combine the numerator and denominator separately. For example, if you have the expression $\frac{2x^2 + 3x^2}{x^2}$, you can simplify it as follows:

${\frac{2x^2 + 3x^2}{x^2} = \frac{(2 + 3)x^2}{x^2} = \frac{5x^2}{x^2} = 5}$

Conclusion

In this article, we have answered some frequently asked questions about simplifying algebraic expressions. We have covered topics such as like terms, combining like terms, and simplifying expressions with multiple variables, negative exponents, and fractions.

Final Answer

The final answer is that simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, you can simplify even the most complex expressions.

Additional Resources

If you want to learn more about simplifying algebraic expressions, here are some additional resources:

• Khan Academy: Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

Practice Problems

Here are some practice problems to help you reinforce your understanding of simplifying algebraic expressions:

1. Simplify the expression $2x^2 + 3x^2 - 4x^2$.
2. Simplify the expression $x^{-2}$.
3. Simplify the expression $\frac{2x^2 + 3x^2}{x^2}$.
4. Simplify the expression $x^2 + 2x^2 + 3x^2$.
5. Simplify the expression $\frac{x^2 + 2x^2}{x^2}$.

I hope this article has been helpful in answering your questions about simplifying algebraic expressions.