How do you simplify $(4sqrt5 + sqrt3)(2sqrt2 - sqrt7)$ ?

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Answer 1 · 2016-01-23T00:12:41

$8sqrt10-4sqrt35+2sqrt6-sqrt21$

Note that $sqrta(sqrtb)=sqrt(ab)$ if $a,b>=0$ .

To simplify this, we can distribute using the foil method.

$overbrace(4sqrt5(2sqrt2))^"First"+overbrace(4sqrt5(-sqrt7))^"Outside"+overbrace(sqrt3(2sqrt2))^"Inside"+overbrace(sqrt3(-sqrt7))^"Last"$

Which, using the first rule, yields

$8sqrt10-4sqrt35+2sqrt6-sqrt21$

How do you simplify (4sqrt5 + sqrt3)(2sqrt2 - sqrt7)(4sqrt5 + sqrt3)(2sqrt2 - sqrt7)?