How do you evaluate #(- 7- \sqrt { 7x } ) ( 4+ 5\sqrt { 7x } )#?

1 Answer
smendyka
Dec 13, 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)(7) - color(red)(sqrt(7x)))(color(blue)(4) + color(blue)(5sqrt(7x)))# becomes:

#(-color(red)(7) xx color(blue)(4)) - (color(red)(7) xx color(blue)(5sqrt(7x))) - (color(red)(sqrt(7x)) xx color(blue)(4)) - (color(red)(sqrt(7x)) xx color(blue)(5sqrt(7x)))#

#-28 - 35sqrt(7x) - 4sqrt(7x) - 5(sqrt(7x))^2#

#-28 - 35sqrt(7x) - 4sqrt(7x) - (5 xx 7x)#

#-28 - 35sqrt(7x) - 4sqrt(7x) - 35x#

We can now combine like terms:

#-28 + (-35 - 4)sqrt(7x) - 35x#

#-28 + (-39)sqrt(7x) - 35x#

#-28 - 39sqrt(7x) - 35x#

#-35x - 39sqrt(7x) - 28#

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