What you’ll learn
Use GCF and distributive property.
Key idea
Divide each addend by the same outside factor; distribute back to check.
A correct outside GCF must multiply each inner term back to its original addend; the sum alone is not the requested factorization.
Worked example
Enter the exact value or ordered values in the format requested below.
Rewrite 6+30 using its greatest common factor outside parentheses. Enter g(u+v), not just the sum.
- The greatest common factor of 6 and 30 is 6.
- 6=6×1 and 30=6×5, so 6+30=6(1+5).
Answer: 6(1+5)
Quick Check
Evaluate a worked attempt at use gcf and distributive property, identify the first invalid step, and provide the correction.
A student writes Step 1: the GCF of 6 and 68 is 2. Step 2: 6+68=2(3+35). Locate the first invalid step and correct the factorization.