Simplify The Expression: 2 X 2 + X − 6 2x^2 + X - 6 2 X 2 + X − 6

Mar 13, 2025 by ADMIN 66 views

**Simplify the Expression: $2x^2 + x - 6$**

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Introduction

In algebra, simplifying expressions is a crucial step in solving equations and inequalities. It involves combining like terms and rearranging the expression to make it easier to work with. In this article, we will simplify the expression $2x^2 + x - 6$ using various techniques.

Understanding the Expression

The given expression is a quadratic expression in the form of $ax^2 + bx + c$ . Here, $a = 2$ , $b = 1$ , and $c = -6$ . To simplify this expression, we need to combine like terms and rearrange the expression to make it easier to work with.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have two like terms: $2x^2$ and $x$ . We can combine these two terms by adding their coefficients.

Step 1: Combine the Like Terms

To combine the like terms, we need to add their coefficients. The coefficient of $2x^2$ is 2, and the coefficient of $x$ is 1. We can add these two coefficients to get:

2x^2 + x = (2 + 1)x^2 = 3x^2

Step 2: Rearrange the Expression

Now that we have combined the like terms, we can rearrange the expression to make it easier to work with. We can rewrite the expression as:

2x^2 + x - 6 = 3x^2 - 6

Simplifying the Expression

Now that we have combined the like terms and rearranged the expression, we can simplify it further. We can factor out the greatest common factor (GCF) of the two terms.

Step 1: Find the GCF

The GCF of $3x^2$ and $-6$ is 3. We can factor out the GCF to get:

3x^2 - 6 = 3(x^2 - 2)

Step 2: Simplify the Expression

Now that we have factored out the GCF, we can simplify the expression further. We can rewrite the expression as:

3(x^2 - 2) = 3x^2 - 6

Conclusion

Final Answer

The final answer is $\boxed{3x^2 - 6}$ .

Example Use Case

Simplifying expressions is an essential skill in algebra. It can be used to solve equations and inequalities, and it can also be used to simplify complex expressions. For example, if we have the expression $4x^2 + 2x - 5$ , we can simplify it using the same techniques we used in this article.

Step 1: Combine the Like Terms

We can combine the like terms $4x^2$ and $2x$ to get:

4x^2 + 2x = (4 + 2)x^2 = 6x^2

Step 2: Rearrange the Expression

We can rewrite the expression as:

4x^2 + 2x - 5 = 6x^2 - 5

Step 3: Simplify the Expression

We can factor out the GCF of $6x^2$ and $-5$ to get:

6x^2 - 5 = 6(x^2 - \frac{5}{6})

Tips and Tricks

Simplifying expressions can be a challenging task, but there are some tips and tricks that can make it easier. Here are a few tips and tricks to keep in mind:

Combine like terms first: Combining like terms is the first step in simplifying an expression. It can help you to identify the GCF and simplify the expression further.
Rearrange the expression: Rearranging the expression can help you to identify the GCF and simplify the expression further.
Factor out the GCF: Factoring out the GCF can help you to simplify the expression further and make it easier to work with.
Use the distributive property: The distributive property can help you to simplify expressions by distributing the coefficients to the variables.

Common Mistakes

Simplifying expressions can be a challenging task, and there are some common mistakes that can occur. Here are a few common mistakes to avoid:

Not combining like terms: Not combining like terms can make it difficult to identify the GCF and simplify the expression further.
Not rearranging the expression: Not rearranging the expression can make it difficult to identify the GCF and simplify the expression further.
Not factoring out the GCF: Not factoring out the GCF can make it difficult to simplify the expression further and make it easier to work with.
Not using the distributive property: Not using the distributive property can make it difficult to simplify expressions and make them easier to work with.

Conclusion

In this article, we simplified the expression $2x^2 + x - 6$ using various techniques. We combined like terms, rearranged the expression, and factored out the greatest common factor (GCF) to simplify the expression. The simplified expression is $3x^2 - 6$ . We also provided some tips and tricks to keep in mind when simplifying expressions, and we discussed some common mistakes to avoid.

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Introduction

In our previous article, we simplified the expression $2x^2 + x - 6$ using various techniques. We combined like terms, rearranged the expression, and factored out the greatest common factor (GCF) to simplify the expression. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to combine like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients. For example, if you have the expression $2x^2 + 3x^2$ , you can combine the like terms by adding their coefficients: $2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$ .

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest factor that divides all the terms in an expression. For example, in the expression $6x^2 + 12x$ , the GCF is 6.

Q: How do I factor out the GCF?

A: To factor out the GCF, you need to divide each term in the expression by the GCF. For example, if you have the expression $6x^2 + 12x$ , you can factor out the GCF by dividing each term by 6: $6x^2 + 12x = 6(x^2 + 2x)$ .

Q: What is the distributive property?

A: The distributive property is a rule that allows you to distribute a coefficient to each term in an expression. For example, if you have the expression $3(x + 2)$ , you can use the distributive property to distribute the coefficient 3 to each term: $3(x + 2) = 3x + 6$ .

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 coefficient to each term in the expression. For example, if you have the expression $4(x + 3)$ , you can use the distributive property to simplify the expression: $4(x + 3) = 4x + 12$ .

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

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

Not combining like terms
Not rearranging the expression
Not factoring out the GCF
Not using the distributive property

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions. We discussed the first step in simplifying an expression, how to combine like terms, the greatest common factor (GCF), how to factor out the GCF, the distributive property, and how to use the distributive property to simplify an expression. We also discussed some common mistakes to avoid when simplifying expressions.

Final Answer

The final answer is $\boxed{3x^2 - 6}$ .

Example Use Case

Step 1: Combine the Like Terms

We can combine the like terms $4x^2$ and $2x$ to get:

4x^2 + 2x = (4 + 2)x^2 = 6x^2

Step 2: Rearrange the Expression

We can rewrite the expression as:

4x^2 + 2x - 5 = 6x^2 - 5

Step 3: Simplify the Expression

We can factor out the GCF of $6x^2$ and $-5$ to get:

6x^2 - 5 = 6(x^2 - \frac{5}{6})

Tips and Tricks

Simplifying expressions can be a challenging task, but there are some tips and tricks that can make it easier. Here are a few tips and tricks to keep in mind:

Combine like terms first: Combining like terms is the first step in simplifying an expression. It can help you to identify the GCF and simplify the expression further.
Rearrange the expression: Rearranging the expression can help you to identify the GCF and simplify the expression further.
Factor out the GCF: Factoring out the GCF can help you to simplify the expression further and make it easier to work with.
Use the distributive property: The distributive property can help you to simplify expressions by distributing the coefficients to the variables.

Common Mistakes

Simplifying expressions can be a challenging task, and there are some common mistakes that can occur. Here are a few common mistakes to avoid:

Not combining like terms: Not combining like terms can make it difficult to identify the GCF and simplify the expression further.
Not rearranging the expression: Not rearranging the expression can make it difficult to identify the GCF and simplify the expression further.
Not factoring out the GCF: Not factoring out the GCF can make it difficult to simplify the expression further and make it easier to work with.
Not using the distributive property: Not using the distributive property can make it difficult to simplify expressions and make them easier to work with.