How do you multiply #(\sqrt { x } - \sqrt { 5} ) ( \sqrt { x } - 6\sqrt { 5} )#?

1 Answer
smendyka
Jan 15, 2018

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)(sqrt(x)) - color(red)(sqrt(5)))(color(blue)(sqrt(x)) - color(blue)(6sqrt(5)))# becomes:

#(color(red)(sqrt(x)) xx color(blue)(sqrt(x))) - (color(red)(sqrt(x)) xx color(blue)(6sqrt(5))) - (color(red)(sqrt(5)) xx color(blue)(sqrt(x))) + (color(red)(sqrt(5)) xx color(blue)(6sqrt(5)))#

#(sqrt(x))^2 - 6sqrt(x)sqrt(5) - sqrt(x)sqrt(5) + 6(sqrt(5))^2#

#x - 6sqrt(5x) - sqrt(5x) + (6 xx 5)#

#x - 6sqrt(5x) - sqrt(5x) + 30#

We can now combine like terms:

#x - 6sqrt(5x) - 1sqrt(5x) + 30#

#x + (-6 - 1)sqrt(5x) + 30#

#x + (-7)sqrt(5x) + 30#

#x - 7sqrt(5x) + 30#

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