Factor completely

4x^3+x^2y-36x-9y

4x³ + x²y - 36x - 9y

4x³ - 36x + x²y - 9y {re-arranged terms}
4x(x² - 9) + y(x² - 9) {factored out GCF's}
(4x + y)(x² - 9) {factored out x² - 9}
(4x + y)(x + 3)(x - 3) {factored the difference of two squares}

- Algebra House

That's way more clever than I was excepting. Thanks!

To factor the given expression completely, we'll start by looking for any common factors in each term.

The given expression is: 4x^3 + x^2y - 36x - 9y

Step 1: Factor out the greatest common factor (GCF)
The GCF of the coefficients is 1, and the GCF of the variables is x.
So, we can factor out x from the first two terms and -9 from the last two terms:

x(4x^2 + xy) - 9(4x + y)

Now the expression becomes: x(4x^2 + xy) - 9(4x + y)

Step 2: Group the terms
Next, we'll group the terms inside the parentheses.

(x + y)(4x^2 + xy) - 9(4x + y)

Step 3: Factor out the GCF from each group
In the first group, we can factor out x:
x(x + y)(4x + y) - 9(4x + y)

Step 4: Check for a common binomial factor
Notice that we have a common binomial factor of (4x + y) in both terms.

So, we can factor it out:

(4x + y)(x(x + y) - 9)

Finally, the given expression is completely factored as:

(4x + y)(x^2 + xy - 9)