Question

Apply the distributive property and the greatest common factor to write an equivalent expression. Enter your answers in the boxes. 105 + 35m = __(__)

Answer 1

The answer is 35(3+m).

To find the GCF, we find the prime factorization of both numbers:

105 = 5*21 = 5*3*7 = 3*5*7
35 = 5*7

Both numbers have the factors 5 and 7, so 5*7=35 is the GCF. This is what we bring out of the parentheses:
35( )

Dividing 105 by 35, we have 5 left over:
35(5+ )

Taking 35 out of 35m, we have m left over:
35(5+m)