How do you factor:
9x^2y^3 - 3x^3y^2 - 15xy
i got: 3xy(3xy^2 - x^2y - 5)
But how do you factor it further to simplify it?
Thx
you could...
3xy ( (xy(3y-x) -5)
but that is not making it simpler
Your answer is correct.
To factor the expression further and simplify it, you can use the common factor method. Let's break down the steps:
1. First, factor out the common factor from all the terms. In this case, the common factor is 3xy, which means we can rewrite the expression as:
3xy(3xy^2 - x^2y - 5)
2. Next, let's focus on factoring the trinomial inside the parentheses, 3xy^2 - x^2y - 5. To factor this, you need to find two binomials that multiply together to give this trinomial.
3. Look for the greatest common factor (GCF) among the three terms in the trinomial. In this case, there is no GCF.
4. Then, check if the trinomial can be factored using any factoring patterns, such as difference of squares or perfect square trinomials. Unfortunately, this trinomial does not fit any of those patterns.
5. Now, you can proceed by using trial and error or the AC method.
a. Trial and error: Try various combinations of factors of the first and last terms (3xy^2 and -5) to see if they add up or subtract to give the middle term (-x^2y). In this case, trial and error might be time-consuming.
b. AC method: Multiply the coefficient of the x^2 term (1) by the constant term (-5) to get -5. Then, find two numbers whose product is -5 and whose sum is the coefficient of the x term (-1). In this case, the numbers are 5 and -1 (5 * -1 = -5, 5 + (-1) = -1).
6. Rewrite the middle term (-x^2y) using the two numbers from step 5, which is -1xy + 5xy, resulting in:
3xy(3xy^2 - x^2y - 5) = 3xy(3xy^2 - 1xy + 5xy - 5)
7. Group the terms together:
3xy[(3xy^2 - 1xy) + (5xy - 5)]
8. Factor out the common factors within each group:
3xy[xy(3y - 1) + 5(5xy - 1)]
9. Finally, you have factored the expression further and simplified it as:
3xy[xy(3y - 1) + 5(5xy - 1)]