Question

How do you simplify `(3sqrt2+sqrt5)(sqrt2-3sqrt(5r))`?

Answer 1

`6 - 9sqrt(10r) + sqrt10 - 15sqrt(r)`

Explanation:

`(3sqrt2 + sqrt5)(sqrt2 - 3sqrt(5r))`

To simplify this, we will use the distributive method called FOIL:

Following this image, we can multiply it out.

The `color(teal)("firsts")`:
`color(teal)(3sqrt2 * sqrt2) = 3sqrt4 = 3*2 = 6`

The `color(indigo)("outers")`:
`color(indigo)(3sqrt2 * -3sqrt(5r)) = 3 * -3 * sqrt(2 * 5r) = -9sqrt(10r)`

The `color(peru)"inners"`:
`color(peru)(sqrt5 * sqrt2) = sqrt(5*2) = sqrt10`

The `color(olivedrab)"lasts"`:
`color(olivedrab)(sqrt5 * -3sqrt(5r)) = -3sqrt(5*5r) = -3sqrt(25r) = -3*5sqrtr = -15sqrtr`

Combine them all together to get your answer:
`6 - 9sqrt(10r) + sqrt10 - 15sqrt(r)`

Hope this helps!