I'm just going to simplify all of our answer choices, and see which one is correct.
a) 2(3h+ 5)(h + 12)
Simplify.
(6h + 10)(h + 12)
Simplify.
(6h · h) + (6h · 12) + (10 · h) + (10 · 12)
Simplify.
6h² + 72h + 10h + 120
Add like terms.
6h² + 82h + 120
So, A IS CORRECT.
However, let's just go through the rest just to make sure.
b) (6h + 12)(h - 10)
Simplify. Because we have already showed you the steps on how to multiply this way, I will just simplify it the faster way, without showing all of the work :)
6h² - 60h + 12h - 120
Add like terms.
6h² - 48h - 120
Therefore, B is incorrect.
c) (6h - 12)(h - 10)
Simplify.
6h² - 60h - 12h + 120
Add like terms.
6h² - 72h + 120
Therefore, C is incorrect as well.
d) (6h - 60)²
Simplify.
(6h - 60)(6h - 60)
Simplify.
36h² - 360 - 360h + 3600
Add like terms.
-324h + 3240
Therefore, D is also incorrect.
Because A is the only one that is equal to 6h² + 82h + 120, it is correct.
