Answer :
Sure, let's factor out the Greatest Common Factor (GCF) from the expression [tex]\(5x + 30y\)[/tex].
Step-by-Step Solution:
1. Identify the GCF of the coefficients:
- The coefficients in the expression are 5 and 30.
- The greatest common factor (GCF) of 5 and 30 is 5.
2. Rewrite each term as a product of the GCF and another factor:
- For the term [tex]\(5x\)[/tex], it can be rewritten as [tex]\(5 \cdot x\)[/tex].
- For the term [tex]\(30y\)[/tex], it can be rewritten as [tex]\(5 \cdot 6y\)[/tex].
3. Factor out the GCF from each term:
- Once we have rewritten each term, we can factor out the common factor, which is 5.
- This means we will write 5 outside the parentheses and include the remaining factors inside the parentheses.
4. Combine the terms inside the parentheses:
- After factoring out 5, the remaining terms inside the parentheses would be [tex]\(x\)[/tex] and [tex]\(6y\)[/tex].
So, the factored expression is:
[tex]\[ 5(x + 6y) \][/tex]
Therefore, the final factored form of the expression [tex]\(5x + 30y\)[/tex] is [tex]\(5(x + 6y)\)[/tex].
Step-by-Step Solution:
1. Identify the GCF of the coefficients:
- The coefficients in the expression are 5 and 30.
- The greatest common factor (GCF) of 5 and 30 is 5.
2. Rewrite each term as a product of the GCF and another factor:
- For the term [tex]\(5x\)[/tex], it can be rewritten as [tex]\(5 \cdot x\)[/tex].
- For the term [tex]\(30y\)[/tex], it can be rewritten as [tex]\(5 \cdot 6y\)[/tex].
3. Factor out the GCF from each term:
- Once we have rewritten each term, we can factor out the common factor, which is 5.
- This means we will write 5 outside the parentheses and include the remaining factors inside the parentheses.
4. Combine the terms inside the parentheses:
- After factoring out 5, the remaining terms inside the parentheses would be [tex]\(x\)[/tex] and [tex]\(6y\)[/tex].
So, the factored expression is:
[tex]\[ 5(x + 6y) \][/tex]
Therefore, the final factored form of the expression [tex]\(5x + 30y\)[/tex] is [tex]\(5(x + 6y)\)[/tex].
