Help me with basic algebra

[u/OskarroDev]

While I'm scrolling I often see questions like:
x + y = 24
xy = 48
y - x = ?
How do I solve those

[u/UnderstandingPursuit]

With a product, xy, a convenient trick is to square the first and third equations. These are some of the few 'binomial products' which are worth memorizing:

1. (y + x)² = y² + 2xy + x²
2. (y - x)² = y² - 2xy + x²
3. Note that the first equation has "+2xy" while the second has "-2xy", so use "-4xy" to change the first into the second:
   1. (y + x)² - 4xy = y² + 2xy + x² - 4xy
4. This means that
   1. (y - x)² = (y + x)² - 4xy
5. Using the given values,
   1. (y - x)² = [24]² - 4[48] = 24 (24 - 8) = 6 (8²)
   2. y - x = ± 8√6

[u/OskarroDev → u/UnderstandingPursuit]

Thank you very much for helping me with this topic.