# How do you simplify (3sqrtx - sqrty)(sqrtx-4sqrty)?

Jul 8, 2016

I found: $3 x + 4 y - 13 \sqrt{x y}$

#### Explanation:

We can try multiplying the two brackets (distribute) to get:
$\left(3 \sqrt{x} - \sqrt{y}\right) \left(\sqrt{x} - 4 \sqrt{y}\right) = 3 \sqrt{x} \sqrt{x} - 12 \sqrt{x} \sqrt{y} - \sqrt{x} \sqrt{y} + 4 \sqrt{y} \sqrt{y} =$
we can now add similar terms (in $\sqrt{x} \sqrt{y}$) and use the fact that $\sqrt{x} \sqrt{x} = x$ or $\sqrt{y} \sqrt{y} = y$ and write:

$= 3 x - 13 \sqrt{x} \sqrt{y} + 4 y = 3 x + 4 y - 13 \sqrt{x y}$

...that is as far I can go!