Tasha believes that she can rewrite the difference 120 - 36 as a product of the two numbers and another difference. Is she correct?

120-36 = 84

84 = 2*2*3*7

See what you can do with that.

(120)(-36)(x) = 120-36

-(36)(120)x = 84
x = -84/(36*120) = -7/360

so all we have to do is write -7/360 as the difference
e.g. -7/360 = 353/360 - 1

so 120 - 36 = (120)(-36)(353/360 - 1)

which is the product of the two numbers and another difference

Yes

To determine whether Tasha is correct, we can start by computing the difference of 120 - 36.

The difference of two numbers is found by subtracting one number from another. In this case, subtracting 36 from 120 gives us:

120 - 36 = 84

Now, Tasha claims that this difference (84) can be expressed as a product of two numbers and another difference. Let's see if this is true.

To express the difference as a product of two numbers, we need to find two numbers whose product gives us 84. We can list all the pairs of numbers that multiply to give 84:

1 x 84 = 84
2 x 42 = 84
3 x 28 = 84
4 x 21 = 84
6 x 14 = 84
7 x 12 = 84

So, we have found six different pairs of numbers whose product is 84.

Now, we need to find another difference among these pairs.

Let's try the first pair:
1 x 84 = 84
So, the first difference is:
84 - 1 = 83

Now let's try the second pair:
2 x 42 = 84
So, the second difference is:
84 - 2 = 82

We can continue this process for all the pairs, finding the difference of each product with 84.

After checking all the pairs, we see that none of the differences equals 84. Therefore, Tasha is incorrect in stating that the difference 120 - 36 can be expressed as a product of the two numbers and another difference.

I don't know what to do