Question

How do you factor `7k(k-3)+4(k-3)`?

Answer 1

`7k(k-3) + 4(k-3) = (7k+4)(k-3)`

Explanation:

The factor `color(blue)((k-3))` occurs in both terms:
`color(white)("XXXX")` `color(red)(7k)color(blue)((k-3))`
`color(white)("XXXX")`and
`color(white)("XXXX")` `color(red)(+4)color(blue)((k-3))`

In general, the distributive property tells us that
`color(white)("XXXX")` `color(red)(a)color(blue)((c))color(red)(+b)color(blue)((c)) = color(red)((a+b))color(blue)((c))`

So, in this case:
`color(white)("XXXX")` `color(red)(7k)color(blue)((k-3))color(red)(+4)color(blue)((k-3)) = color(red)((7k+4))color(blue)((k-3))`