The answer choices appear to be indicating that we must apply the distributive property to find our simplified expression. To apply the distributive property, we must multiply the number outside of the parenthesis by all numbers inside of the parenthesis.
For example;
2(1 + 3) Multiply 2 by all numbers inside of the parenthesis separately.
2(1) + 2(3) 2 + 6 8.
Now that we've explained and (hopefully) understand the concept of our problem, let's prepare to solve.
We have the following expression and answer choices: 96 + 36
A.) 4(24 + 9) B.) 6(16 + 6) C.) 12(8 + 3) D.) 18(5 + 2)
Before we proceed to solve for this, let's evaluate our question carefully.
"Tonya uses the greatest common factor and the distributive property to rewrite this sum: 96 + 36"
Now, let's list the factors out from each number.
96;
1 x 96 2 x 48 3 x 32 4 x 24 6 x 16 8 x 12
36;
1 x 36 2 x 18 3 x 12 4 x 9 6 x 6
Now that we've listed our factors, let's take a look and see which answer choices contain our factors and which don't.
A, B, and C all list factors that are shown above. However, D doesn't as it has "5", which we do not have any numbers that end in 5 or 0, so we can remove answer choice "D" off of our list.
We are now remaining with answer choices A, B, and C.
Since the question requests that we use the greatest common factor, let's take a look into our factors and see which one is the greatest.
The greatest common factor is "12", so we should look for the answer choice that best matches 12.
Answer choice "C" is the only answer choice that contains our greatest common factor, 12.
