Select The Correct Answer.What Is The Simplified Form Of This Expression? \left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right ]A. 3 X 2 − 2 X + 4 3x^2 - 2x + 4 3 X 2 − 2 X + 4 B. 7 X 2 − 2 X + 4 7x^2 - 2x + 4 7 X 2 − 2 X + 4 C. 3 X 2 + 6 X + 4 3x^2 + 6x + 4 3 X 2 + 6 X + 4 D. 9 − 2 X − 2 X 2 9 - 2x - 2x^2 9 − 2 X − 2 X 2

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Introduction

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Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will guide you through the process of simplifying a given expression, using the example of $\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right)$. We will break down the expression into smaller parts, apply the rules of algebra, and arrive at the simplified form.

Understanding the Expression

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The given expression is a combination of two algebraic expressions, which are being subtracted from each other. To simplify this expression, we need to apply the rules of algebra, which include combining like terms and rearranging the expression.

Like Terms

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Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are:

• $5x^2$ and $-2x^2$
• $2x$ and $-4x$
• $11$ and $7$

Distributive Property

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The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We can use this property to simplify the expression by distributing the negative sign to each term inside the second set of parentheses.

Simplifying the Expression

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Using the distributive property, we can rewrite the expression as:

$\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2$

Now, we can combine like terms by adding or subtracting the coefficients of the like terms.

Combining Like Terms

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Combining the like terms, we get:

$5x^2 + 2x + 11 - 7 - 4x + 2x^2 = (5x^2 + 2x^2) + (2x - 4x) + (11 - 7)$

Simplifying further, we get:

$(5x^2 + 2x^2) + (2x - 4x) + (11 - 7) = 7x^2 - 2x + 4$

Conclusion

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In this article, we simplified the given expression $\left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right)$ using the rules of algebra. We applied the distributive property to simplify the expression and combined like terms to arrive at the simplified form. The final answer is:

$\boxed{7x^2 - 2x + 4}$

Final Answer

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The final answer is $\boxed{7x^2 - 2x + 4}$.

Discussion

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This problem requires the application of algebraic rules and techniques to simplify a given expression. The distributive property and the concept of like terms are essential in simplifying the expression. The final answer is a simplified form of the given expression, which can be used in various mathematical applications.

Related Topics

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• Algebraic expressions
• Distributive property
• Like terms
• Simplifying expressions

Example Use Cases

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• Simplifying algebraic expressions in calculus
• Solving systems of linear equations
• Finding the maximum or minimum value of a function

Tips and Tricks

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• Always apply the distributive property when simplifying expressions.
• Identify like terms and combine them to simplify the expression.
• Use the rules of algebra to rearrange the expression and arrive at the simplified form.

Common Mistakes

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• Failing to apply the distributive property
• Not identifying like terms
• Not combining like terms correctly

Conclusion

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Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the final answer. The final answer is $\boxed{7x^2 - 2x + 4}$.

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Introduction

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Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in simplifying algebraic expressions.

Q&A

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Q: What is the distributive property, and how is it used in simplifying algebraic expressions?

A: The distributive property is a rule in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property is used to simplify expressions by distributing the negative sign to each term inside the second set of parentheses.

Q: What are like terms, and how are they combined in simplifying algebraic expressions?

A: Like terms are terms that have the same variable raised to the same power. In simplifying algebraic expressions, like terms are combined by adding or subtracting their coefficients.

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

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $3x^2 + 2x^2$, the like terms are $3x^2$ and $2x^2$.

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

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

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions 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.

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

A: To simplify an algebraic expression with multiple sets of parentheses, follow these steps:

1. Distribute the negative sign to each term inside the second set of parentheses.
2. Combine like terms.
3. Simplify the expression further if possible.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Failing to apply the distributive property
• Not identifying like terms
• Not combining like terms correctly
• Not following the order of operations

Example Problems

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Problem 1

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Simplify the expression $\left(2x^2 + 3x + 1\right) - \left(4x^2 - 2x + 3\right)$.

Solution

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Using the distributive property, we can rewrite the expression as:

$\left(2x^2 + 3x + 1\right) - \left(4x^2 - 2x + 3\right) = 2x^2 + 3x + 1 - 4x^2 + 2x - 3$

Combining like terms, we get:

$2x^2 + 3x + 1 - 4x^2 + 2x - 3 = -2x^2 + 5x - 2$

Problem 2

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Simplify the expression $\left(3x^2 - 2x + 1\right) + \left(2x^2 + 4x - 3\right)$.

Solution

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Using the distributive property, we can rewrite the expression as:

$\left(3x^2 - 2x + 1\right) + \left(2x^2 + 4x - 3\right) = 3x^2 - 2x + 1 + 2x^2 + 4x - 3$

Combining like terms, we get:

$3x^2 - 2x + 1 + 2x^2 + 4x - 3 = 5x^2 + 2x - 2$

Conclusion

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Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By following the distributive property and combining like terms, we can simplify expressions and arrive at the final answer. Remember to avoid common mistakes and follow the order of operations to ensure accurate results.

Final Answer

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The final answer is $\boxed{7x^2 - 2x + 4}$.

Discussion

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This Q&A guide provides a comprehensive overview of the concepts and techniques involved in simplifying algebraic expressions. By following the steps outlined in this guide, you can simplify expressions and arrive at the final answer.

Related Topics

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• Algebraic expressions
• Distributive property
• Like terms
• Simplifying expressions

Example Use Cases

---

• Simplifying algebraic expressions in calculus
• Solving systems of linear equations
• Finding the maximum or minimum value of a function

Tips and Tricks

---

• Always apply the distributive property when simplifying expressions.
• Identify like terms and combine them to simplify the expression.
• Use the rules of algebra to rearrange the expression and arrive at the simplified form.

Common Mistakes

---

• Failing to apply the distributive property
• Not identifying like terms
• Not combining like terms correctly
• Not following the order of operations