Answer :
To factor out the greatest common factor (GCF) from the expression [tex]\( 12 + 20 \)[/tex] using the distributive property, follow these steps:
1. Identify the greatest common factor (GCF) of the numbers 12 and 20:
- List the factors of each number.
- Factors of 12: [tex]\( 1, 2, 3, 4, 6, 12 \)[/tex]
- Factors of 20: [tex]\( 1, 2, 4, 5, 10, 20 \)[/tex]
- Find the greatest factor that both numbers share.
- Common factors of 12 and 20: [tex]\( 1, 2, 4 \)[/tex]
- The greatest common factor is [tex]\( 4 \)[/tex].
2. Rewrite each term as a product of the GCF and another number:
- Express 12 and 20 in terms of the GCF:
- [tex]\( 12 = 4 \times 3 \)[/tex]
- [tex]\( 20 = 4 \times 5 \)[/tex]
3. Apply the distributive property to factor out the GCF:
- Combine the terms using the distributive property, which states [tex]\( a \times b + a \times c = a(b + c) \)[/tex]:
- [tex]\( 12 + 20 = 4 \times 3 + 4 \times 5 \)[/tex]
- Factor out the common factor 4: [tex]\( 4(3 + 5) \)[/tex]
Therefore, the expression [tex]\( 12 + 20 \)[/tex] factored by the greatest common factor using the distributive property is:
[tex]\[ 12 + 20 = 4(3 + 5) \][/tex]
1. Identify the greatest common factor (GCF) of the numbers 12 and 20:
- List the factors of each number.
- Factors of 12: [tex]\( 1, 2, 3, 4, 6, 12 \)[/tex]
- Factors of 20: [tex]\( 1, 2, 4, 5, 10, 20 \)[/tex]
- Find the greatest factor that both numbers share.
- Common factors of 12 and 20: [tex]\( 1, 2, 4 \)[/tex]
- The greatest common factor is [tex]\( 4 \)[/tex].
2. Rewrite each term as a product of the GCF and another number:
- Express 12 and 20 in terms of the GCF:
- [tex]\( 12 = 4 \times 3 \)[/tex]
- [tex]\( 20 = 4 \times 5 \)[/tex]
3. Apply the distributive property to factor out the GCF:
- Combine the terms using the distributive property, which states [tex]\( a \times b + a \times c = a(b + c) \)[/tex]:
- [tex]\( 12 + 20 = 4 \times 3 + 4 \times 5 \)[/tex]
- Factor out the common factor 4: [tex]\( 4(3 + 5) \)[/tex]
Therefore, the expression [tex]\( 12 + 20 \)[/tex] factored by the greatest common factor using the distributive property is:
[tex]\[ 12 + 20 = 4(3 + 5) \][/tex]
