How do you simplify $(3 \sqrt{x} - \sqrt{y}) (\sqrt{x} - 4 \sqrt{y})$ $(3sqrtx - sqrty)(sqrtx-4sqrty)$ ?

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How do you simplify $(3 \sqrt{x} - \sqrt{y}) (\sqrt{x} - 4 \sqrt{y})$ $(3sqrtx - sqrty)(sqrtx-4sqrty)$ ?

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Answer 1 · 2016-07-08T19:28:20

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

Explanation:

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

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

...that is as far I can go!

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How do you simplify $(3 \sqrt{x} - \sqrt{y}) (\sqrt{x} - 4 \sqrt{y})$ $(3sqrtx - sqrty)(sqrtx-4sqrty)$ ?

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How do you simplify (3sqrtx - sqrty)(sqrtx-4sqrty)(3√x−√y)(√x−4√y)(3sqrtx - sqrty)(sqrtx-4sqrty)?

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How do you simplify $(3 \sqrt{x} - \sqrt{y}) (\sqrt{x} - 4 \sqrt{y})$ $(3sqrtx - sqrty)(sqrtx-4sqrty)$ ?