How do you simplify (4 sqrt7 - 8 sqrt 5) (5sqrt7 + 10sqrt 5)?

1 Answer
smendyka
Jun 9, 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)(4sqrt(7)) - color(red)(8sqrt(5)))(color(blue)(5sqrt(7)) + color(blue)(10sqrt(5))) becomes:

(color(red)(4sqrt(7)) xx color(blue)(5sqrt(7))) + (color(red)(4sqrt(7)) xx color(blue)(10sqrt(5))) - (color(red)(8sqrt(5)) xx color(blue)(5sqrt(7))) - (color(red)(8sqrt(5)) xx color(blue)(10sqrt(5)))

(20 xx 7) + (40(color(red)(sqrt(7)) xx color(blue)(sqrt(5)))) - (40(color(red)(sqrt(5)) xx color(blue)(sqrt(7)))) - (80 xx 5)

140 + (40(color(red)(sqrt(7)) xx color(blue)(sqrt(5)))) - (40(color(red)(sqrt(5)) xx color(blue)(sqrt(7)))) - 400

We can now group and combine like terms:

140 - 400 + (40(color(red)(sqrt(7)) xx color(blue)(sqrt(5)))) - (40(color(red)(sqrt(5)) xx color(blue)(sqrt(7))))

(140 - 400) + (40 - 40)(color(red)(sqrt(7)) xx color(blue)(sqrt(5)))

-260 + 0(color(red)(sqrt(7)) xx color(blue)(sqrt(5)))

-260 + 0

-260

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