Simplify The Expression: $2x(3x + 4) - 3(3x + 4$\]

$$

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the rules of algebra. In this article, we will simplify the given expression $2x(3x + 4) - 3(3x + 4)$ using the distributive property and combining like terms. We will also provide step-by-step solutions and explanations to help readers understand the process.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. In the given expression, we have two sets of parentheses: $2x(3x + 4)$ and $-3(3x + 4)$. We can use the distributive property to expand each set of parentheses.

Distributive Property Formula

The distributive property formula is:

$a(b + c) = ab + ac$

where $a$, $b$, and $c$ are algebraic expressions.

Applying the Distributive Property

Let's apply the distributive property to the given expression:

$2x(3x + 4) - 3(3x + 4)$

Using the distributive property, we can expand each set of parentheses:

$2x(3x + 4) = 2x(3x) + 2x(4)$

$-3(3x + 4) = -3(3x) - 3(4)$

Simplifying each expression, we get:

$2x(3x + 4) = 6x^2 + 8x$

$-3(3x + 4) = -9x - 12$

Combining Like Terms

Now that we have expanded each set of parentheses, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

Combining Like Terms Formula

The formula for combining like terms is:

$a + b = a + b$

where $a$ and $b$ are like terms.

Combining Like Terms

Let's combine like terms in the given expression:

$6x^2 + 8x - 9x - 12$

Combining like terms, we get:

$6x^2 - x - 12$

Final Answer

The simplified expression is:

$6x^2 - x - 12$

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a deep understanding of the rules of algebra. In this article, we simplified the given expression $2x(3x + 4) - 3(3x + 4)$ using the distributive property and combining like terms. We provided step-by-step solutions and explanations to help readers understand the process.

Tips and Tricks

• Always use the distributive property to expand expressions.
• Combine like terms to simplify expressions.
• Use the distributive property formula to expand expressions.
• Use the combining like terms formula to simplify expressions.

Frequently Asked Questions

• 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 inside the parentheses with the term outside the parentheses.
• Q: How do I apply the distributive property? A: To apply the distributive property, multiply each term inside the parentheses with the term outside the parentheses.
• Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.

References

• Algebraic Expressions
• Distributive Property
• Combining Like Terms

Related Articles

• Simplifying Algebraic Expressions
• Distributive Property Examples
• Combining Like Terms Examples
  

$$

Introduction

In our previous article, we simplified the expression $2x(3x + 4) - 3(3x + 4)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions related to simplifying algebraic 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 inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, multiply each term inside the parentheses with the term outside the parentheses. For example, in the expression $2x(3x + 4)$, we multiply $2x$ with each term inside the parentheses: $2x(3x) + 2x(4)$.

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 $6x^2 + 8x - 9x - 12$, the terms $8x$ and $-9x$ 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, add or subtract the coefficients of the like terms. For example, in the expression $6x^2 + 8x - 9x - 12$, we combine the like terms $8x$ and $-9x$ by adding their coefficients: $8x - 9x = -x$.

Q: What is the difference between the distributive property and combining like terms?

A: The distributive property is used to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. Combining like terms is used to simplify expressions by adding or subtracting the coefficients of like terms.

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

A: To simplify an expression with multiple sets of parentheses, use the distributive property to expand each set of parentheses, and then combine like terms.

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

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

• Not using the distributive property to expand expressions
• Not combining like terms
• Adding or subtracting unlike terms
• Not following the order of operations (PEMDAS)

Tips and Tricks

• Always use the distributive property to expand expressions.
• Combine like terms to simplify expressions.
• Use the distributive property formula to expand expressions.
• Use the combining like terms formula to simplify expressions.
• Be careful when adding or subtracting unlike terms.

Frequently Asked Questions

• 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 inside the parentheses with the term outside the parentheses.
• Q: How do I apply the distributive property? A: To apply the distributive property, multiply each term inside the parentheses with the term outside the parentheses.
• Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.

References

• Algebraic Expressions
• Distributive Property
• Combining Like Terms

Related Articles

• Simplifying Algebraic Expressions
• Distributive Property Examples
• Combining Like Terms Examples