How do you simplify # (sqrt5+4)(sqrt5-1)#?

2 Answers
Apr 10, 2017

Answer:

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(5)) + color(red)(4))(color(blue)(sqrt(5)) - color(blue)(1))# becomes:

#(color(red)(sqrt(5)) xx color(blue)(sqrt(5))) - (color(red)(sqrt(5)) xx color(blue)(1)) + (color(red)(4) xx color(blue)(sqrt(5))) - (color(red)(4) xx color(blue)(1))#

#(sqrt(5))^2 - sqrt(5) + 4sqrt(5) - 4#

#5 - sqrt(5) + 4sqrt(5) - 4#

We can now group and combine like terms:

#5 - 4 - 1sqrt(5) + 4sqrt(5)#

#(5 - 4) + (-1 + 4)sqrt(5)#

#1 + 3sqrt(5)#

Or

#3sqrt(5) + 1#

Apr 10, 2017

Answer:

#1+3sqrt(5)#

Explanation:

#(sqrt(5)+4)(sqrt(5)-1)=#

#=5-sqrt(5)+4sqrt(5)-4=#

#=1+3sqrt(5)#