Question

How do you factor `18b^2+24bt+8t^2`?

Answer 1

Given `18b^2+24bt+8t^2`

If you extract the obvious common factor of `2`
`color(white)("XXXX")` `2(9b^2+12bt+4t^2)`
`color(white)("XXXX")` `=2((3b)^2 + 2(3b)(2t) + (2t)^2)`
we end up with some obvious squares for the first and last terms and using their roots can see that together they will generate the middle term.
`color(white)("XXXX")` `2(3b+2t)^2`