Question

How do you factor by grouping `4b^2+4bc+c^2-16`?

Answer 1

`(2b+c+4)*(2b+c-4)`

Explanation:

`color(red)(4b^2+4bc+c^2) - color(blue)(16)`
rewrite the frist 3 terms as a square
`color(white)("XXXX")` `color(red)((2b+c)^2) - color(blue)(4^2)`
this is the difference of squares with a well-know factoring
`color(white)("XXXX")` `(2b+c+4)*(2b+c-4)`