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

2 Answers
Jul 9, 2017

Answer:

It needs plain multiplication.

Explanation:

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

Jul 9, 2017

Answer:

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)#