Can (4x^3)y - 9xy^3 factor?
Take out the obvious common factor xy:
(4x^3)y - 9xy^3
=xy(4x^2 - 9y^2)
and factor as difference of two squares
=xy((2x)²-(3y)²)
=xy(2x+3y)(2x-3y)
To determine if the expression (4x^3)y - 9xy^3 can be factored, we need to look for any common factors between the terms.
The expression can be rewritten as 4x^3 * y - 9 * x * y^3.
Looking at the two terms, we can see that both terms have a factor of y. So, we can factor out the common factor of y:
y(4x^3 - 9xy^2).
Now let's look at the remaining terms inside the parentheses. We can see that both terms have a factor of x, so we can factor out the common factor of x as well:
y * x * (4x^2 - 9y^2).
Now, we have factored the expression as y * x * (4x^2 - 9y^2).
Therefore, the expression (4x^3)y - 9xy^3 can be factored as y * x * (4x^2 - 9y^2).