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

1 Answer
Gió
Jul 8, 2016

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

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)=#
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:

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

...that is as far I can go!

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