How do you simplify #3y sqrt (4y^3) - sqrt (16y^4) + sqrt( 18y^3)#?
Before doing any manipulations, let's determine the domain of this expression.
The only "restrictive" operation here is an operation of the square root that is defined in the field of real numbers only for non-negative arguments.
So, the domain is determined by an inequality
Now we can simplify this expression using a simple transformation that is true for non-negative numbers:
Using this, notice that
Combining these expression with their corresponding coefficients, produces: