We can solve this question using matching operations (my favorite Quantitative Comparison strategy)

Given:
Quantity A: \(xy+2\)
Quantity B: \((x+7)(y-3)\)

Use the FOIL method to expand Quantity B to get:
Quantity A: \(xy+2\)
Quantity B: \(xy-3x+7y-21\)

Subtract \(xy\) from both quantities:
Quantity A: \(2\)
Quantity B: \(-3x+7y-21\)

Add \(21\) from both quantities:
Quantity A: \(23\)
Quantity B: \(-3x+7y\)

At this point, it's clear that the correct answer is D. Here's why:
If \(x=0\) and \(y = 0\), then Quantity A is greater
If \(x=0\) and \(y = 100\), then Quantity B is greater

Answer: D

RELATED VIDEO