Question

How do you factor `10a b + 14a + 5b + 7` completely?

Answer 1

`(5b+7)(2a+1)`

Explanation:

We can get a clue as to how to solve this by noting that we can pair terms `(10ab, 5b)` and `(14a,7)` and that each pair will have the same internal ratio `2a:1`

`10ab+14a+5b+7`
`color(white)("XXX")=color(magenta)(""(10ab+5b)) + color(blue)(""(14a+7))`

`color(white)("XXX")=color(magenta)(5b(2a+1))+color(blue)(7(2a+1))`

`color(white)("XXX")=(5b+7)(2a+1)`