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

2 Answers
Apr 11, 2018

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.

Apr 11, 2018

=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.