Question

Find the product.

`(7sqrt(3) - 4)(5sqrt(3) + 1)`

Answer 1

To find the product:

`(7sqrt(3) - 4)(5sqrt(3) + 1)`

Use distributive property (FOIL method):

`7sqrt(3) xx 5sqrt(3) + 7sqrt(3) xx 1 - 4 xx 5sqrt(3) - 4 xx 1`

Now compute each term:

`7sqrt(3) xx 5sqrt(3) = 35 xx 3 = 105`

`7sqrt(3) xx 1 = 7sqrt(3)`

`-4 xx 5sqrt(3) = -20sqrt(3)`

–4 × 1 = –4

Now combine:

`105 + 7sqrt(3) - 20sqrt(3) - 4`

= `(105 - 4) + (-13sqrt(3))`

= `101 - 13sqrt(3)`