#( sqrt 3 + 2 sqrt 10) (4 sqrt 3 - sqrt 10)# How to multiply?

1 Answer
smendyka
Apr 12, 2017

See the entire 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)(sqrt(3)) + color(red)(2sqrt(10)))(color(blue)(4sqrt(3)) - color(blue)(sqrt(10)))# becomes:

#(color(red)(sqrt(3)) xx color(blue)(4sqrt(3))) - (color(red)(sqrt(3)) xx color(blue)(sqrt(10))) + (color(red)(2sqrt(10)) xx color(blue)(4sqrt(3))) - (color(red)(2sqrt(10)) xx color(blue)(sqrt(10)))#

#4(sqrt(3))^2 - sqrt(30) + 8sqrt(30) - 2(sqrt(10))^2#

#(4 * 3) - sqrt(30) + 8sqrt(30) - (2 * 10)#

#12 - sqrt(30) + 8sqrt(30) - 20#

We can now group and combine like terms:

#12 - 20 - 1sqrt(30) + 8sqrt(30)#

#(12 - 20) + (-1 + 8)sqrt(30)#

#-8 + 7sqrt(30)#

Or

#7sqrt(30) - 8#

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