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

2 Answers
Sunayan S
Jul 9, 2017

It needs plain multiplication.

Explanation:

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

smendyka
Jul 9, 2017

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)

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