Simplify The Expression: { (3x + 2)(3x - 2)$}$

$$

=====================================================

Introduction

---

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the most common methods of simplifying expressions is by using the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this article, we will use the distributive property to simplify the expression $(3x + 2)(3x - 2)$.

The Distributive Property

---

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression. The distributive property can be written as:

a(b + c) = ab + ac

This property can be applied to any real numbers a, b, and c. In the expression $(3x + 2)(3x - 2)$, we can use the distributive property to expand the expression.

Expanding the Expression

---

To expand the expression $(3x + 2)(3x - 2)$, we need to multiply each term in the first expression by each term in the second expression. Using the distributive property, we get:

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

Simplifying the Expression

---

Now that we have expanded the expression, we can simplify it by combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have the following like terms:

• $(3x)(3x) = 9x^2$
• $(3x)(-2) = -6x$
• $(2)(3x) = 6x$
• $(2)(-2) = -4$

Combining these like terms, we get:

$9x^2 - 6x + 6x - 4$

Canceling Out Like Terms

---

Now that we have combined the like terms, we can cancel out any terms that have the same variable raised to the same power. In this case, we have the following like terms:

• $-6x$ and $6x$ have the same variable raised to the same power, so we can cancel them out.

Canceling out these like terms, we get:

$9x^2 - 4$

Conclusion

---

In this article, we used the distributive property to simplify the expression $(3x + 2)(3x - 2)$. We expanded the expression by multiplying each term in the first expression by each term in the second expression, and then simplified it by combining like terms. Finally, we canceled out any terms that had the same variable raised to the same power. The simplified expression is $9x^2 - 4$.

Example Use Case

---

The expression $(3x + 2)(3x - 2)$ can be used to solve equations and inequalities. For example, if we have the equation $(3x + 2)(3x - 2) = 0$, we can use the simplified expression $9x^2 - 4$ to solve for x.

Tips and Tricks

---

• When simplifying expressions, always use the distributive property to expand the expression.
• When combining like terms, always combine terms that have the same variable raised to the same power.
• When canceling out like terms, always cancel out terms that have the same variable raised to the same power.

Common Mistakes

---

• Not using the distributive property to expand the expression.
• Not combining like terms.
• Not canceling out like terms.

Final Answer

---

The final answer is $9x^2 - 4$.

$$

=====================================================

Introduction

---

In our previous article, we used the distributive property to simplify the expression $(3x + 2)(3x - 2)$. We expanded the expression by multiplying each term in the first expression by each term in the second expression, and then simplified it by combining like terms. In this article, we will answer some common questions related to simplifying expressions.

Q&A

---

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression. The distributive property can be written as:

a(b + c) = ab + ac

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

A: To use the distributive property to simplify expressions, you need to multiply each term in one expression by each term in another expression. For example, to simplify the expression $(3x + 2)(3x - 2)$, you would multiply each term in the first expression by each term in the second expression.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression $2x + 3x$, the terms $2x$ and $3x$ are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, in the expression $2x + 3x$, you would combine the like terms by adding the coefficients, which would give you $5x$.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different properties in algebra. The distributive property allows us to expand expressions by multiplying each term in one expression by each term in another expression. The commutative property, on the other hand, allows us to rearrange the order of the terms in an expression without changing the value of the expression.

Q: Can I use the distributive property to simplify expressions with variables and constants?

A: Yes, you can use the distributive property to simplify expressions with variables and constants. For example, to simplify the expression $(2x + 3)(4x - 1)$, you would multiply each term in the first expression by each term in the second expression.

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

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

• Not using the distributive property to expand the expression
• Not combining like terms
• Not canceling out like terms
• Not following the order of operations

Example Use Cases

---

The distributive property can be used to solve equations and inequalities. For example, if we have the equation $(3x + 2)(3x - 2) = 0$, we can use the simplified expression $9x^2 - 4$ to solve for x.

Tips and Tricks

---

• Always use the distributive property to expand expressions.
• Always combine like terms.
• Always cancel out like terms.
• Always follow the order of operations.

Common Mistakes

---

• Not using the distributive property to expand the expression.
• Not combining like terms.
• Not canceling out like terms.
• Not following the order of operations.

Final Answer

---

The final answer is $9x^2 - 4$.