Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Our platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
Let’s focus on simplifying the task of finding the prime factorizations step-by-step.
### 1) Prime Factorization of [tex]\( 16y \)[/tex]:
First, let's separate 16 and [tex]\( y \)[/tex]:
- The number 16 can be broken down into its prime factors.
- [tex]\( y \)[/tex] is already a prime number if it’s considered a variable.
Step-by-Step Factorization:
- We start with 16: [tex]\( 16 = 2 \times 8 \)[/tex]
- Factor 8 further: [tex]\( 8 = 2 \times 4 \)[/tex]
- Factor 4 further: [tex]\( 4 = 2 \times 2 \)[/tex]
So, combining all the factors, we get:
[tex]\[ 16 = 2 \times 2 \times 2 \times 2 = 2^4 \][/tex]
Thus, the prime factorization of [tex]\( 16y \)[/tex]:
[tex]\[ 16y = 2^4 \cdot y \][/tex]
### 2) Prime Factorization of [tex]\( 4v \)[/tex]:
First, let's separate 4 and [tex]\( v \)[/tex]:
- The number 4 can be broken down into its prime factors.
- [tex]\( v \)[/tex] is a prime number if it's considered a variable.
Step-by-Step Factorization:
- We start with 4: [tex]\( 4 = 2 \times 2 \)[/tex]
Thus, the prime factorization of [tex]\( 4v \)[/tex]:
[tex]\[ 4v = 2^2 \cdot v \][/tex]
### 3) Interpret and Correct Provided Expressions:
The given expressions seem disjointed and possibly incorrect, making it hard to interpret directly. However, let's confirm known prime factorizations before moving on to specific needs.
### 4) Prime Factorization of [tex]\( 21x^2 \)[/tex]:
First, let's separate 21 and [tex]\( x^2 \)[/tex]:
- The number 21 can be broken down into its prime factors.
- [tex]\( x^2 \)[/tex] is considered as [tex]\( x \cdot x \)[/tex].
Step-by-Step Factorization:
- We start with 21: [tex]\( 21 = 3 \times 7 \)[/tex]
Thus, the prime factorization of [tex]\( 21x^2 \)[/tex]:
[tex]\[ 21x^2 = 3 \times 7 \times x \times x \][/tex]
Recap of all the prime factorizations:
1. [tex]\( 16y = 2^4 \cdot y \)[/tex]
2. [tex]\( 4v = 2^2 \cdot v \)[/tex]
3. [tex]\( 21x^2 = 3 \times 7 \times x^2 \)[/tex]
Now, the problem seems to involve manipulation beyond basic prime factorization, potentially leading us to algebraic simplifications or fraction forms. But with the given terms taken into account, we reiterate:
- Factor each numeric element distinctly.
- Maintain each distinct algebraic element alongside to convey full intentions.
Let me know if you need specific breakdowns or assistance across further equations from initial expressions!
### 1) Prime Factorization of [tex]\( 16y \)[/tex]:
First, let's separate 16 and [tex]\( y \)[/tex]:
- The number 16 can be broken down into its prime factors.
- [tex]\( y \)[/tex] is already a prime number if it’s considered a variable.
Step-by-Step Factorization:
- We start with 16: [tex]\( 16 = 2 \times 8 \)[/tex]
- Factor 8 further: [tex]\( 8 = 2 \times 4 \)[/tex]
- Factor 4 further: [tex]\( 4 = 2 \times 2 \)[/tex]
So, combining all the factors, we get:
[tex]\[ 16 = 2 \times 2 \times 2 \times 2 = 2^4 \][/tex]
Thus, the prime factorization of [tex]\( 16y \)[/tex]:
[tex]\[ 16y = 2^4 \cdot y \][/tex]
### 2) Prime Factorization of [tex]\( 4v \)[/tex]:
First, let's separate 4 and [tex]\( v \)[/tex]:
- The number 4 can be broken down into its prime factors.
- [tex]\( v \)[/tex] is a prime number if it's considered a variable.
Step-by-Step Factorization:
- We start with 4: [tex]\( 4 = 2 \times 2 \)[/tex]
Thus, the prime factorization of [tex]\( 4v \)[/tex]:
[tex]\[ 4v = 2^2 \cdot v \][/tex]
### 3) Interpret and Correct Provided Expressions:
The given expressions seem disjointed and possibly incorrect, making it hard to interpret directly. However, let's confirm known prime factorizations before moving on to specific needs.
### 4) Prime Factorization of [tex]\( 21x^2 \)[/tex]:
First, let's separate 21 and [tex]\( x^2 \)[/tex]:
- The number 21 can be broken down into its prime factors.
- [tex]\( x^2 \)[/tex] is considered as [tex]\( x \cdot x \)[/tex].
Step-by-Step Factorization:
- We start with 21: [tex]\( 21 = 3 \times 7 \)[/tex]
Thus, the prime factorization of [tex]\( 21x^2 \)[/tex]:
[tex]\[ 21x^2 = 3 \times 7 \times x \times x \][/tex]
Recap of all the prime factorizations:
1. [tex]\( 16y = 2^4 \cdot y \)[/tex]
2. [tex]\( 4v = 2^2 \cdot v \)[/tex]
3. [tex]\( 21x^2 = 3 \times 7 \times x^2 \)[/tex]
Now, the problem seems to involve manipulation beyond basic prime factorization, potentially leading us to algebraic simplifications or fraction forms. But with the given terms taken into account, we reiterate:
- Factor each numeric element distinctly.
- Maintain each distinct algebraic element alongside to convey full intentions.
Let me know if you need specific breakdowns or assistance across further equations from initial expressions!
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.
