How do you simplify $(3 sqrt(x^3)) times (4 + 2 sqrt(xy))$ ?

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Answer 1 · 2018-01-08T12:24:29

See a solution process below:

First, multiply each term within the right parenthesis by the term on the left:

$(color(red)(3sqrt(x^3))) xx (4 + 2sqrt(xy)) =>$

$(color(red)(3sqrt(x^3)) xx 4) + (color(red)(3sqrt(x^3)) xx 2sqrt(xy)) =>$

$12sqrt(x^3) + 6sqrt(x^3)sqrt(xy)$

Next, we can use this rule to combine the radicals in the term on the right:

$sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))$

$12sqrt(x^3) + 6sqrt(color(red)(x^3))sqrt(color(blue)(xy)) =>$

$12sqrt(x^3) + 6sqrt(color(red)(x^3) * color(blue)(xy)) =>$

$12sqrt(x^3) + 6sqrt(x^4y)$

Then, we can use the opposite of the above rule to reduce the radicals:

$sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))$

$12sqrt(x^3) + 6sqrt(x^4y) =>$

$12sqrt(color(red)(x^2) * color(blue)(x)) + 6sqrt(color(red)(x^4) * color(blue)(y)) =>$

$12sqrt(color(red)(x^2))sqrt(color(blue)(x)) + 6sqrt(color(red)(x^4))sqrt(color(blue)(y)) =>$

$12xsqrt(x) + 6x^2sqrt(y)$

How do you simplify (3 sqrt(x^3)) times (4 + 2 sqrt(xy)) (3 sqrt(x^3)) times (4 + 2 sqrt(xy))?