Which Expression Is Equivalent To $16a + 24b$?A. $4(4a + 20b$\] B. $8(2a + 3b$\] C. $4a(4 + 6b$\] D. $8ab(2 + 3$\]

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Introduction

In algebra, we often need to simplify expressions by factoring out common terms. This can help us to rewrite an expression in a more compact and easier-to-understand form. In this article, we will explore which expression is equivalent to $16a + 24b$.

Understanding the Expression

The given expression is $16a + 24b$. To simplify this expression, we need to find the greatest common factor (GCF) of the two terms. The GCF of 16 and 24 is 8.

Factoring Out the GCF

We can factor out the GCF of 8 from both terms:

$$16a + 24b = 8(2a) + 8(3b)$$

Simplifying the Expression

Now, we can simplify the expression by combining the two terms:

$$8(2a) + 8(3b) = 8(2a + 3b)$$

Comparing with the Options

Let's compare the simplified expression with the options:

A. $4(4a + 20b)$ B. $8(2a + 3b)$ C. $4a(4 + 6b)$ D. $8ab(2 + 3)$

Option B is the Correct Answer

The simplified expression $8(2a + 3b)$ matches option B. Therefore, the correct answer is:

Conclusion

In this article, we simplified the expression $16a + 24b$ by factoring out the GCF and combining the terms. We then compared the simplified expression with the options and found that option B is the correct answer. This demonstrates the importance of factoring and simplifying expressions in algebra.

Key Takeaways

• The greatest common factor (GCF) of 16 and 24 is 8.
• We can factor out the GCF of 8 from both terms: $16a + 24b = 8(2a) + 8(3b)$.
• The simplified expression is $8(2a + 3b)$.
• Option B is the correct answer.

Additional Practice

To practice simplifying expressions, try the following exercises:

• Simplify the expression $20x + 30y$.
• Simplify the expression $12a + 18b$.
• Simplify the expression $15x + 25y$.

References

• Algebraic Expressions
• Factoring
• Simplifying Expressions

Related Topics

• Algebraic Identities
• Factoring Quadratics
• Simplifying Rational Expressions
  Q&A: Simplifying Algebraic Expressions =====================================

Introduction

In our previous article, we explored how to simplify the expression $16a + 24b$ by factoring out the greatest common factor (GCF). In this article, we will answer some frequently asked questions (FAQs) about simplifying algebraic expressions.

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

A: The greatest common factor (GCF) of two or more numbers is the largest number that divides each of the numbers without leaving a remainder. In the case of the expression $16a + 24b$, the GCF is 8.

Q: How do I find the GCF of two numbers?

A: To find the GCF of two numbers, you can use the following steps:

1. List the factors of each number.
2. Identify the common factors.
3. Choose the greatest common factor.

For example, to find the GCF of 16 and 24, you can list the factors of each number:

• Factors of 16: 1, 2, 4, 8, 16
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors are 1, 2, 4, and 8. The greatest common factor is 8.

Q: How do I simplify an expression by factoring out the GCF?

A: To simplify an expression by factoring out the GCF, you can follow these steps:

1. Identify the GCF of the terms in the expression.
2. Factor out the GCF from each term.
3. Combine the terms.

For example, to simplify the expression $16a + 24b$, you can factor out the GCF of 8:

$$16a + 24b = 8(2a) + 8(3b)$$

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

A: Factoring and simplifying an expression are related but distinct concepts.

Factoring an expression involves breaking it down into its component parts, such as factoring a quadratic expression into the product of two binomials.

Simplifying an expression involves reducing it to its simplest form, such as combining like terms or factoring out the GCF.

Q: Can I simplify an expression without factoring it out?

A: Yes, you can simplify an expression without factoring it out. For example, you can combine like terms or use the distributive property to simplify an expression.

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

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

• Forgetting to factor out the GCF.
• Not combining like terms.
• Using the distributive property incorrectly.
• Not checking for common factors.

Conclusion

In this article, we answered some frequently asked questions about simplifying algebraic expressions. We discussed the importance of finding the greatest common factor (GCF) and factoring it out to simplify an expression. We also covered some common mistakes to avoid when simplifying expressions.

Key Takeaways

• The greatest common factor (GCF) is the largest number that divides each of the numbers without leaving a remainder.
• To simplify an expression by factoring out the GCF, you can factor out the GCF from each term and combine the terms.
• Factoring and simplifying an expression are related but distinct concepts.
• You can simplify an expression without factoring it out by combining like terms or using the distributive property.

Additional Practice

To practice simplifying expressions, try the following exercises:

• Simplify the expression $20x + 30y$.
• Simplify the expression $12a + 18b$.
• Simplify the expression $15x + 25y$.

References

• Algebraic Expressions
• Factoring
• Simplifying Expressions

Related Topics

• Algebraic Identities
• Factoring Quadratics
• Simplifying Rational Expressions