Question

How do you simplify `(-3sqrt(3k)+4)(sqrt(3k)-5)`?

Answer 1

`-9k+ 19sqrt(3k)-20`

Explanation:

`(-3sqrt(3k) +4)(sqrt(3k)-5)` or

`-3sqrt(3k)*sqrt(3k)+3sqrt(3k)*5+4*sqrt(3k) -4*5` or

`-3*3k +15sqrt(3k)+4sqrt(3k)-20` or

`-9k+ 19sqrt(3k)-20` [Ans]

Answer 2

`-9k+19sqrt3k-20`

Explanation:

`"multiply each term in the second factor by each term"`
`"in the first factor"`

`rArr(color(red)(-3sqrt(3k)+4))(sqrt(3k)-5)`

`=color(red)(-3sqrt(3k))(sqrt(3k)-5)color(red)(+4)(sqrt(3k)-5)`

`"distributing gives "`

`• " note that "sqrtaxxsqrta=a`

`=-9k+15sqrt(3k)+4sqrt(3k)-20`

`=-9k+19sqrt(3k)-20`