...and perhaps the answer choices can help
It might be helpful to sometimes look at the answer choices as "part" of the question.
182^2 - 142^2
When you see something like this many of you may recognize a^2 - b^2 and directly solve it. Others, however, may actually do this a harder way which is to do 182 times 182 and then subtract 142 times 142.
Suppose you didn't know the formula though and really didn't want to do the long method either.
It might be helpful to check out the answer choices for some inspiration.
If all the answer choices end with a different unit digit you've got a very easy path to solve this sort of question. Simply look for the answer choice that ends with a 0.
If all the answer choices are different in terms of length (i.e. 10, 100, 1000) you can also ballpark your calculations to get a rough idea which it might be. 182 is close to 180 --> 32400. 142 is close to 150 --> 22500 ---> So the answer is roughly around 10,000.
If, for example, you find yourself stuck with two answer choices that share a single units digit, simply look for the one closer to 10,000.
The point of this post is to perhaps give the answer choices a quick look through to see if they can help you out. In an odd way, the real goal is to "select" the correct answer choice - not necessarily solve the math.