or and the distributive property to write 28+12 as a product?

Question

Which expression uses the greatest common factor and the distributive property to write 28+12 as a product?

10 points

2(14+6)

8(20+4)

4(7+3)

7(4+5)

Answer 1

The distributive property tells us that we can write an equation in the format ab + bc as a(b+c). All of the possible answers for this question are in the a(b+c) format.

Let's look at the answer choices and find out which ones are equal to 28+12 or 40:

2(14+6) = 2x14+2x6 = 28+12

8(20+4) = 8x20+8x4 = 160+32

4(7+3) = 4x7 + 4x3 = 28 + 12

7(4+5) = 7x4+7x5 = 28 + 35

So, let's now look at the greatest common factor. Let's find the greatest common factor of 28 and 12.

Factors of 28: 1, 2, 4, 7,14, 28

Factors of 12: 1, 2, 3, 4, 6, 12

Greatest factor that both 12 and 28 have in common: 4

Since 4 is common to both of the multiplication expressions, we can factor that out when rewriting using the distributive property.

4x7 + 4x3 = 4(7+3)

This matches one of the two possible answer choices, so we know it is correct.