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

Question

Hazel Anglin · Accepted Answer

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)#

Savannah Anderson · Answer

undefined To simplify the expression (3 sqrt(x^3)) times (4 + 2 sqrt(xy)), you can use the distributive property. First, multiply 3 sqrt(x^3) by 4, which gives you 12 sqrt(x^3). Then, multiply 3 sqrt(x^3) by 2 sqrt(xy), resulting in 6 sqrt(x^3y). Finally, combine the two terms to get the simplified expression: 12 sqrt(x^3) + 6 sqrt(x^3y).