Simplify The Expression: $9x^2 - 4$

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Introduction

In algebra, simplifying expressions is a crucial step in solving equations and inequalities. It involves combining like terms and eliminating any unnecessary components. In this article, we will focus on simplifying the expression $9x^2 - 4$. We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is $9x^2 - 4$. This expression consists of two terms: $9x^2$ and $-4$. The first term is a quadratic term, which is a polynomial of degree two, while the second term is a constant term.

Simplifying the Expression

To simplify the expression $9x^2 - 4$, we need to combine like terms. In this case, there are no like terms, as the first term is a quadratic term and the second term is a constant term. However, we can rewrite the expression in a more simplified form by factoring out the greatest common factor (GCF) of the two terms.

Factoring Out the GCF

The GCF of $9x^2$ and $-4$ is 1, as there is no common factor other than 1. However, we can rewrite the expression as:

$$9x^2 - 4 = (3x)^2 - 2^2$$

This is a difference of squares, which can be factored as:

$$(3x)^2 - 2^2 = (3x + 2)(3x - 2)$$

Simplified Form

The simplified form of the expression $9x^2 - 4$ is:

$$(3x + 2)(3x - 2)$$

This is the final simplified form of the expression.

Conclusion

In this article, we simplified the expression $9x^2 - 4$ by factoring out the GCF and rewriting it as a difference of squares. We then factored the difference of squares to obtain the final simplified form of the expression. This process involved combining like terms and eliminating any unnecessary components.

Example Use Cases

The simplified expression $(3x + 2)(3x - 2)$ can be used in various mathematical applications, such as:

• Solving quadratic equations
• Finding the roots of a quadratic equation
• Simplifying complex expressions

Tips and Tricks

When simplifying expressions, it is essential to:

• Identify like terms and combine them
• Factor out the GCF of the terms
• Rewrite the expression in a more simplified form

By following these tips and tricks, you can simplify expressions efficiently and effectively.

Common Mistakes to Avoid

When simplifying expressions, it is essential to avoid common mistakes, such as:

• Failing to identify like terms
• Not factoring out the GCF
• Not rewriting the expression in a more simplified form

By avoiding these common mistakes, you can simplify expressions accurately and efficiently.

Final Thoughts

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Introduction

In our previous article, we simplified the expression $9x^2 - 4$ by factoring out the GCF and rewriting it as a difference of squares. We then factored the difference of squares to obtain the final simplified form of the expression. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q: What is the difference between simplifying and solving an expression?

A: Simplifying an expression involves combining like terms and eliminating any unnecessary components, while solving an expression involves finding the value of the expression.

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

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

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

A: The GCF of two terms is the largest factor that divides both terms without leaving a remainder. For example, the GCF of $6x^2$ and $9x^2$ is $3x^2$.

Q: How do I factor out the GCF of two terms?

A: To factor out the GCF of two terms, you need to divide both terms by the GCF. For example, if the GCF of $6x^2$ and $9x^2$ is $3x^2$, you can factor out the GCF by dividing both terms by $3x^2$:

$$\frac{6x^2}{3x^2} = 2$$

$$\frac{9x^2}{3x^2} = 3$$

So, the factored form of the expression $6x^2 + 9x^2$ is $3x^2(2 + 3)$.

Q: What is a difference of squares?

A: A difference of squares is an expression of the form $a^2 - b^2$, where $a$ and $b$ are any real numbers. The difference of squares can be factored as $(a + b)(a - b)$.

Q: How do I factor a difference of squares?

A: To factor a difference of squares, you need to identify the values of $a$ and $b$ in the expression $a^2 - b^2$. Then, you can factor the expression as $(a + b)(a - b)$.

Q: What is the final simplified form of the expression $9x^2 - 4$?

A: The final simplified form of the expression $9x^2 - 4$ is $(3x + 2)(3x - 2)$.

Q: Can I use the simplified expression $(3x + 2)(3x - 2)$ to solve quadratic equations?

A: Yes, you can use the simplified expression $(3x + 2)(3x - 2)$ to solve quadratic equations. For example, if you have a quadratic equation of the form $ax^2 + bx + c = 0$, you can substitute the values of $a$, $b$, and $c$ into the simplified expression and solve for $x$.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We covered topics such as identifying like terms, factoring out the GCF, and factoring a difference of squares. We also provided examples and explanations to help you understand the concepts better. By following the steps outlined in this article, you can simplify expressions efficiently and effectively.

Tips and Tricks

When simplifying expressions, it is essential to:

• Identify like terms and combine them
• Factor out the GCF of the terms
• Rewrite the expression in a more simplified form
• Use the simplified expression to solve quadratic equations

By following these tips and tricks, you can simplify expressions accurately and efficiently.

Common Mistakes to Avoid

When simplifying expressions, it is essential to avoid common mistakes, such as:

• Failing to identify like terms
• Not factoring out the GCF
• Not rewriting the expression in a more simplified form
• Not using the simplified expression to solve quadratic equations

By avoiding these common mistakes, you can simplify expressions accurately and efficiently.

Final Thoughts

Simplifying expressions is a crucial step in solving equations and inequalities. By following the steps outlined in this article, you can simplify expressions efficiently and effectively. Remember to identify like terms, factor out the GCF, and rewrite the expression in a more simplified form. With practice and patience, you can become proficient in simplifying expressions and tackle complex mathematical problems with confidence.