How do you simplify (3sqrtx - sqrty)(sqrtx-4sqrty)(3xy)(x4y)?

1 Answer
Jul 8, 2016

I found: 3x+4y-13sqrt(xy)3x+4y13xy

Explanation:

We can try multiplying the two brackets (distribute) to get:
(3sqrt(x)-sqrt(y))(sqrt(x)-4sqrt(y))=3sqrt(x)sqrt(x)-12sqrt(x)sqrt(y)-sqrt(x)sqrt(y)+4sqrt(y)sqrt(y)=(3xy)(x4y)=3xx12xyxy+4yy=
we can now add similar terms (in sqrt(x)sqrt(y)xy) and use the fact that sqrt(x)sqrt(x)=xxx=x or sqrt(y)sqrt(y)=yyy=y and write:

=3x-13sqrt(x)sqrt(y)+4y=3x+4y-13sqrt(xy)=3x13xy+4y=3x+4y13xy

...that is as far I can go!