Question

How do you simplify `(4+3sqrt3) (9-2sqrt3)`?

Answer 1

It needs plain multiplication.

Explanation:

`(4+3sqrt3)(9-2sqrt3)`
`=(4×9)-(4×2sqrt3)+(9×3sqrt3)-(3sqrt3×2sqrt3)`
`=18+19sqrt3`

Answer 2

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(4) + color(red)(3sqrt(3)))(color(blue)(9) - color(blue)(2sqrt(3)))` becomes:

`(color(red)(4) xx color(blue)(9)) - (color(red)(4) xx color(blue)(2sqrt(3))) + (color(red)(3sqrt(3)) xx color(blue)(9)) - (color(red)(3sqrt(3)) xx color(blue)(2sqrt(3)))`

`36 - 8sqrt(3) + 27sqrt(3) - 6(sqrt(3)sqrt(3))`

`36 - 8sqrt(3) + 27sqrt(3) - (6 * 3)`

`36 - 8sqrt(3) + 27sqrt(3) - 18`

Now, we can group and combine like terms:

`36 - 18 - 8sqrt(3) + 27sqrt(3)`

`(36 - 18) + (-8 + 27)sqrt(3)`

`18 + 19sqrt(3)`