Question

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

Answer 1

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`