Question

Which expression is equivalent to 15n−24?




5(3n−8)

15(n−24)

3(5n−8)

3n(5−8)

Answer 1

Hi!

To solve this, find the GCM (greatest common multiple) of 15 and 24.

We can do this by finding the prime factorization. 

15/3 = 5
3·5

24/2 = 12
12/2 = 6
6/2 = 3
2·2·2·3

Both prime factorizations have the number 3 in common. So the GCM is 3. 

Divide both numbers by 3.
15n/3 = 5n
-24/3 = -8

Since the GCM is 3, 3 goes outside the parentheses. 

The numbers that go inside the parentheses are 5n-8

The answer is 3(5n-8)

You can check your answer by using the distribution property.
3·5n = 15n
3·(-8) = -24
15n-24

Hope this helps!