Hey there!
If we want to understand this problem, we have to understand the keywords. We want to know what the words mean so we can use the definition and solve the problem.
The distributive property is a property in math for multiplication and it's defined as:
a(b+c) = ab + ac
Next, a factor is a number that when multiplied by another gives the specified or needed number. For example, two is a factor of four because two times two is four.
We want the greatest common factor of both. So, we can list the factors of both 16 and 36 and find the greatest common one. Remember, according to our formula, this GCF would be the a in a(b+c). It would be the number that goes into both.
16 - 1, 2, 4, 8, 16
36- 1, 2, 3, 4, 6, 9
It looks as if the greatest common factor is 4. Therefore, we know our a value is 4. We have:
4(b+c) = 16+36
We know a(b+c) = ab + ac.
Therefore, we want to plug in the values of b and c the number of times 4 goes into 16 and 36. That means we have:
4(4+9) = 16 + 36
16 + 36 = 16 + 36
We're right! :)
Hope this helps!
