A portion of the house collapsed because the contractor __________ and built it with very poor quality materials.

This sentence describes a situation in which a portion of a house collapsed due to the contractor's negligence or unethical shortcuts during construction. For the blank, therefore, we need an idiomatic expression that reflects cutting costs inappropriately and has a negative connotation since poor quality led to the collapse. Option B (Cut corners) fits perfectly in this situation, as it means to do something poorly or in a cheap way to save time or money. 

The other options either don’t match the meaning or are not appropriate in this context. Option A (Short-changed places) is not a proper idiom. Option C (Bit the bullet) means to endure something unpleasant; however, that is not relevant to what is being asked here. Option D (Made a fortune) means to make a lot of money; this is also irrelevant to the context of the sentence (substandard house construction)

The correct answer is therefore Option B - cut corners