Select The Correct Answer.Which Expression Is Equivalent To The Given Expression? − 2 X 2 + 8 X − 9 + 4 X + 7 X 2 + 2 -2x^2 + 8x - 9 + 4x + 7x^2 + 2 − 2 X 2 + 8 X − 9 + 4 X + 7 X 2 + 2 A. − 5 X 2 + 4 X + 11 -5x^2 + 4x + 11 − 5 X 2 + 4 X + 11 B. − 9 X 2 + 4 X − 7 -9x^2 + 4x - 7 − 9 X 2 + 4 X − 7 C. − 9 X 2 − 12 X + 11 -9x^2 - 12x + 11 − 9 X 2 − 12 X + 11 D. 5 X 2 + 12 X − 7 5x^2 + 12x - 7 5 X 2 + 12 X − 7

Understanding the Problem

In this article, we will focus on simplifying algebraic expressions by combining like terms. We will use the given expression $-2x^2 + 8x - 9 + 4x + 7x^2 + 2$ and compare it with the options provided to determine the correct equivalent expression.

What are Like Terms?

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

• $-2x^2$ and $7x^2$ (both have the variable $x$ raised to the power of 2)
• $8x$ and $4x$ (both have the variable $x$ raised to the power of 1)
• $-9$ and $2$ (both are constants)

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can start by combining the like terms with the variable $x$ raised to the power of 2:

$-2x^2 + 7x^2 = 5x^2$

Next, we can combine the like terms with the variable $x$ raised to the power of 1:

$8x + 4x = 12x$

Finally, we can combine the constants:

$-9 + 2 = -7$

The Simplified Expression

Now that we have combined the like terms, we can write the simplified expression:

$5x^2 + 12x - 7$

Comparing with the Options

Let's compare the simplified expression with the options provided:

A. $-5x^2 + 4x + 11$ B. $-9x^2 + 4x - 7$ C. $-9x^2 - 12x + 11$ D. $5x^2 + 12x - 7$

The only option that matches the simplified expression is:

D. $5x^2 + 12x - 7$

Conclusion

In this article, we simplified the given expression by combining like terms. We identified the like terms, combined them, and wrote the simplified expression. We then compared the simplified expression with the options provided and determined that the correct equivalent expression is:

D. $5x^2 + 12x - 7$

Tips and Tricks

• When simplifying algebraic expressions, it's essential to identify and combine like terms.
• Use the distributive property to expand expressions and combine like terms.
• Check your work by plugging in values for the variables and evaluating the expression.

Common Mistakes

• Failing to identify like terms and combine them.
• Not using the distributive property to expand expressions.
• Not checking the work by plugging in values for the variables.

Real-World Applications

Simplifying algebraic expressions is a crucial skill in various fields, including:

• Physics: Simplifying expressions is essential in solving problems involving motion, energy, and forces.
• Engineering: Simplifying expressions is necessary in designing and analyzing complex systems.
• Computer Science: Simplifying expressions is used in algorithms and data structures.

Practice Problems

1. Simplify the expression: $3x^2 + 2x - 5 + 4x^2 - 3x + 2$
2. Simplify the expression: $2x^2 - 3x + 1 + 5x^2 + 2x - 3$
3. Simplify the expression: $x^2 + 2x - 4 + 3x^2 - 2x + 1$

Answer Key

1. $7x^2 - x + 3$
2. $7x^2 + x - 2$
3. $4x^2 + 0x - 3$

References

• Algebraic Expressions
• Simplifying Algebraic Expressions
• Distributive Property
  Simplifying Algebraic Expressions: A Q&A Guide =====================================================

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In the expression $2x^2 + 3x + 4$, the terms $2x^2$ and $3x$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms. This involves adding or subtracting the coefficients of the like terms. For example, in the expression $2x^2 + 3x + 4$, you can combine the like terms $2x^2$ and $3x$ to get $5x^2$.

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that a single term can be distributed to multiple terms. For example, in the expression $2(x + 3)$, the term $2$ can be distributed to the terms $x$ and $3$ to get $2x + 6$.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, you need to distribute the single term to the multiple terms. For example, in the expression $2(x + 3)$, you can distribute the term $2$ to the terms $x$ and $3$ to get $2x + 6$.

Q: What is the order of operations?

A: The order of operations is a set of rules that determines the order in which mathematical operations should be performed. The order of operations is:

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

Q: How do I apply the order of operations to simplify an expression?

A: To apply the order of operations to simplify an expression, you need to follow the order of operations. For example, in the expression $2(x + 3) + 4$, you need to evaluate the expression inside the parentheses first, then distribute the term $2$ to the terms $x$ and $3$, and finally add $4$ to the result.

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 identify like terms and combine them.
• Not using the distributive property to expand expressions.
• Not checking the work by plugging in values for the variables.
• Not following the order of operations.

Q: How do I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you need to plug in values for the variables and evaluate the expression. For example, if you simplify the expression $2x^2 + 3x + 4$ to get $5x^2 + 6$, you can plug in the value $x = 2$ to get $20 + 6 = 26$. If the result is not equal to the original expression, then you made a mistake.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Some real-world applications of simplifying algebraic expressions include:

• Physics: Simplifying expressions is essential in solving problems involving motion, energy, and forces.
• Engineering: Simplifying expressions is necessary in designing and analyzing complex systems.
• Computer Science: Simplifying expressions is used in algorithms and data structures.

Q: How do I practice simplifying algebraic expressions?

A: To practice simplifying algebraic expressions, you can try the following:

• Simplify expressions on your own.
• Use online resources and practice problems.
• Work with a partner or tutor to practice simplifying expressions.
• Take practice tests and quizzes to assess your skills.

Q: What are some resources for learning more about simplifying algebraic expressions?

A: Some resources for learning more about simplifying algebraic expressions include:

• Online tutorials and videos.
• Textbooks and workbooks.
• Online practice problems and quizzes.
• Tutoring and online courses.
• Math websites and forums.