y=2x^3√9-x^2

To simplify the expression y = 2x^3√(9 - x^2), we can start by factoring the expression inside the square root (√).

Step 1: Factor the expression inside the square root (√)
The expression 9 - x^2 can be factored as a difference of squares:
9 - x^2 = (3)^2 - (x)^2
= (3 + x)(3 - x)

Step 2: Rewrite the expression y = 2x^3√(9 - x^2) using the factored form:
y = 2x^3√((3 + x)(3 - x))

Step 3: Simplify the expression inside the square root (√)
The expression (√((3 + x)(3 - x))) can be further simplified to:
(√(3 + x)) (√(3 - x))

Now, the simplified expression becomes y = 2x^3(√(3 + x))(√(3 - x)).

This is the simplified form of the given expression y = 2x^3√(9 - x^2).