First, multiply each term within the right parenthesis by the term on the left:
(color(red)(3sqrt(x^3))) xx (4 + 2sqrt(xy)) =>(3√x3)×(4+2√xy)⇒
(color(red)(3sqrt(x^3)) xx 4) + (color(red)(3sqrt(x^3)) xx 2sqrt(xy)) =>(3√x3×4)+(3√x3×2√xy)⇒
12sqrt(x^3) + 6sqrt(x^3)sqrt(xy)12√x3+6√x3√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))√a⋅√b=√a⋅b
12sqrt(x^3) + 6sqrt(color(red)(x^3))sqrt(color(blue)(xy)) =>12√x3+6√x3√xy⇒
12sqrt(x^3) + 6sqrt(color(red)(x^3) * color(blue)(xy)) =>12√x3+6√x3⋅xy⇒
12sqrt(x^3) + 6sqrt(x^4y)12√x3+6√x4y
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))√a⋅b=√a⋅√b
12sqrt(x^3) + 6sqrt(x^4y) =>12√x3+6√x4y⇒
12sqrt(color(red)(x^2) * color(blue)(x)) + 6sqrt(color(red)(x^4) * color(blue)(y)) =>12√x2⋅x+6√x4⋅y⇒
12sqrt(color(red)(x^2))sqrt(color(blue)(x)) + 6sqrt(color(red)(x^4))sqrt(color(blue)(y)) =>12√x2√x+6√x4√y⇒
12xsqrt(x) + 6x^2sqrt(y)12x√x+6x2√y
