Question

How do you simplify `(5+4sqrt3)(3+sqrt3)`?

Answer 1

Foil and combine like terms

Explanation:

Start by foiling. You should get `15+5sqrt3+12sqrt3+12`. If you're not sure how I got 12 it's because when you multiply roots they cancel so `sqrt3` times `sqrt3` became 3, and that 3 got multiplied by the 4 to become 12. Once you have `15+5sqrt3+12sqrt3+12`, you have to combine like terms so you get `17sqrt3+27`.

Answer 2

`=17sqrt3+27`

Explanation:

Using the FOIL method, you can multiply the two terms together using the numbers inside each set of parenthesis.

`(5+4sqrt3)(3+sqrt3)`

F means "first terms."

`5*3=15`

I means "inner terms."

`4sqrt3*3=12sqrt3`

O means "outer terms."

`5*sqrt3=5sqrt3`

Finally, L means "last terms."

`4sqrt3*sqrt3=4*3=12`

Add your four results together and simplify to complete the foil.

`15+12sqrt3+5sqrt3+12`

`=17sqrt3+27`

That is the expanded form.