Factor $72y + 108z$ To Identify The Equivalent Expressions. Choose 2 Answers:A. 9 ( 8 Y + 12 Z 9(8y + 12z 9 ( 8 Y + 12 Z ] B. 36 ( 2 Y + 3 Z 36(2y + 3z 36 ( 2 Y + 3 Z ] C. 6 ( 12 Y + 18 Z 6(12y + 18z 6 ( 12 Y + 18 Z ] D. 12 ( 6 Y + 9 Z 12(6y + 9z 12 ( 6 Y + 9 Z ]

Introduction

Factorizing algebraic expressions is a fundamental concept in mathematics that helps us simplify complex expressions and solve equations. In this article, we will focus on factorizing the expression $72y + 108z$ to identify its equivalent expressions. We will explore the different methods of factorization and provide step-by-step solutions to help you understand the concept better.

What is Factorization?

Factorization is the process of expressing an algebraic expression as a product of simpler expressions. It involves breaking down a complex expression into its prime factors, which can be multiplied together to obtain the original expression. Factorization is an essential tool in mathematics, as it helps us simplify complex expressions, solve equations, and identify patterns.

Methods of Factorization

There are several methods of factorization, including:

• Common Factor Method: This method involves identifying the common factors in an expression and factoring them out.
• Grouping Method: This method involves grouping the terms in an expression and factoring out the common factors from each group.
• Difference of Squares Method: This method involves factoring expressions that can be written as the difference of two squares.

Factorizing the Expression $72y + 108z$

To factorize the expression $72y + 108z$, we can use the common factor method. The first step is to identify the greatest common factor (GCF) of the two terms. In this case, the GCF is 36.

# Factorizing the Expression $72y + 108z$
Step 1: Identify the Greatest Common Factor (GCF)
The GCF of $72y$ and $108z$ is 36.
Step 2: Factor out the GCF
$72y + 108z = 36(2y + 3z)$

Equivalent Expressions

Now that we have factored the expression $72y + 108z$, we can identify its equivalent expressions. The equivalent expressions are:

• $9(8y + 12z)$
• $36(2y + 3z)$
• $6(12y + 18z)$
• $12(6y + 9z)$

To verify that these expressions are equivalent, we can multiply them out and compare the results.

# Equivalent Expressions
Step 1: Multiply out the expressions
$9(8y + 12z) = 72y + 108z$
$36(2y + 3z) = 72y + 108z$
$6(12y + 18z) = 72y + 108z$
$12(6y + 9z) = 72y + 108z$
Step 2: Compare the results
All the expressions are equivalent, as they produce the same result when multiplied out.

Conclusion

In this article, we factorized the expression $72y + 108z$ using the common factor method and identified its equivalent expressions. We also explored the different methods of factorization and provided step-by-step solutions to help you understand the concept better. Factorization is an essential tool in mathematics, and it helps us simplify complex expressions, solve equations, and identify patterns.

Final Answer

The equivalent expressions for $72y + 108z$ are:

• $9(8y + 12z)$
• $36(2y + 3z)$
• $6(12y + 18z)$
• $12(6y + 9z)$

Introduction

In our previous article, we explored the concept of factorizing algebraic expressions and factorized the expression $72y + 108z$ using the common factor method. In this article, we will provide a Q&A guide to help you understand the concept better and address any questions you may have.

Q: What is factorization?

A: Factorization is the process of expressing an algebraic expression as a product of simpler expressions. It involves breaking down a complex expression into its prime factors, which can be multiplied together to obtain the original expression.

Q: Why is factorization important?

A: Factorization is an essential tool in mathematics, as it helps us simplify complex expressions, solve equations, and identify patterns. It is used in various fields, including algebra, geometry, and calculus.

Q: What are the different methods of factorization?

A: There are several methods of factorization, including:

• Common Factor Method: This method involves identifying the common factors in an expression and factoring them out.
• Grouping Method: This method involves grouping the terms in an expression and factoring out the common factors from each group.
• Difference of Squares Method: This method involves factoring expressions that can be written as the difference of two squares.

Q: How do I factorize an expression?

A: To factorize an expression, follow these steps:

1. Identify the greatest common factor (GCF) of the terms in the expression.
2. Factor out the GCF from each term.
3. Simplify the expression by combining like terms.

Q: What are equivalent expressions?

A: Equivalent expressions are expressions that produce the same result when evaluated. They are often used to simplify complex expressions and solve equations.

Q: How do I identify equivalent expressions?

A: To identify equivalent expressions, follow these steps:

1. Factorize the expression using the common factor method or other methods.
2. Simplify the expression by combining like terms.
3. Compare the results to identify equivalent expressions.

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

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

• Not identifying the greatest common factor (GCF): Make sure to identify the GCF of the terms in the expression.
• Not factoring out the GCF: Factor out the GCF from each term to simplify the expression.
• Not combining like terms: Combine like terms to simplify the expression.

Q: How do I practice factorizing expressions?

A: To practice factorizing expressions, try the following:

• Start with simple expressions: Begin with simple expressions and gradually move on to more complex ones.
• Use online resources: Utilize online resources, such as worksheets and practice problems, to help you practice factorizing expressions.
• Seek help when needed: Don't hesitate to ask for help if you're struggling with a particular expression.

Conclusion

In this article, we provided a Q&A guide to help you understand the concept of factorizing algebraic expressions better. We addressed common questions and provided tips and tricks to help you practice factorizing expressions. Factorization is an essential tool in mathematics, and with practice, you can become proficient in factorizing expressions.

Final Tips

• Practice regularly: Regular practice will help you become proficient in factorizing expressions.
• Seek help when needed: Don't hesitate to ask for help if you're struggling with a particular expression.
• Use online resources: Utilize online resources, such as worksheets and practice problems, to help you practice factorizing expressions.