simplify the radicals and collect like terms
√96y^3 + 2y√384y - √150y^3
To simplify the radicals, we can find the smallest perfect squares that divide each term under the square roots.
√96y^3 = √(16 * 6 * y^2 * y) = 4y√6y
√384y = √(64 * 6 * y) = 8√6y
√150y^3 = √(25 * 6 * y^2 * y) = 5y√6y
Now, we can rewrite the expression:
4y√6y + 2y * 8√6y - 5y√6y
Combining like terms:
12y√6y - 5y√6y
Finally,
7y√6y