Question

#(4 sqrt 3xy^3) (-2 sqrt 6x^3y^2)? #Multiply the radical expression

Answer 1

`-24sqrt(2)x^4y^5`

Explanation:

`(4sqrt(3)xy^3)(-2sqrt(6)x^3y^2)`

decomposing each factor:
`color(white)("XXX")=(4xxsqrt(3)xx x xx y^3)xx((-2) xx sqrt(6) xx x^3 xx y^2)`

regrouping like factors:
`color(white)("XXX")=(4 xx(-2))xx(sqrt(3)xxsqrt(6))xx(x xx x^3)xx(y^3 xxy^2)`

combining like factors:
`color(white)("XXX")=(-8) xx (sqrt(18)) xx (x^4) xx (y^5)`

simplifying the `sqrt(18)` factor
`color(white)("XXX")=(-8) xx (3sqrt(2)) xx (x^4) xx (y^5)`

combining the two constant factors
`color(white)("XXX")=(-24sqrt(2)) xx (x^4) xx (y^5)`

back into (compressed) standard form:
`color(white)("XXX")=-24sqrt(2)x^4y^5`