Question

How do you factor by grouping `mn - 4m - 5n + 20`?

Answer 1

`mn-4m-5n+20`

`= (mn-4m)-(5n-20)`

`=m(n-4)-5(n-4)`

`=(m-5)(n-4)`

Answer 2

Given `mn-4m -5n+20`
Notice that by extracting a common factor from the first 2 terms and a (different) common factor from the last 2 terms, we are left with `(n-4)` in both cases;
so
`color(red)(mn-4m) color(blue)(-5n+20)`

`=color(red)(m(n-4))color(blue)(-5(n-4))`

`=(m-5)(n-4)`