1. ## Homework Help

What does 5(x)^2y(3x+2y)+15xy(3x+2y)(x-3y) factor out to?

2. Originally Posted by andy011789
What does 5(x)^2y(3x+2y)+15xy(3x+2y)(x-3y) factor out to?
what are the common terms you see here? pull them out, what do you get?

3. ## Common Terms

The common terms I see are the (3x+2y) which would leave (3x+2y)[(5x^2y+15xy(x-3y)], but I am not sure where to go from there. But then I also see there is 5xy, I am not sure what to do with it or where to put it. Unless I leave it how it is, but I don't think it is completely factored

4. Originally Posted by andy011789
The common terms I see are the (3x+2y) which would leave (3x+2y)[(5x^2y+15xy(x-3y)], but I am not sure where to go from there. But then I also see there is 5xy, I am not sure what to do with it or where to put it. Unless I leave it how it is, but I don't think it is completely factored
ok, so we see that 5xy is common also then. so pull that out. we get:

$\displaystyle 5xy(3x + 2y) \left[x + 3(x - 3y) \right]$

what else can we do here?

5. well there is still an x in each term in the brackets, so I would imagine we should take it out. but I am still not entirely sure what to do after that or if removing the x is valid. Which would leave x(5xy)(3x+2y)[3-3y]

6. Hello, Andy!

Factor: .$\displaystyle 5x^2y(3x+2y)+15xy(3x+2y)(x-3y)$

We have: .$\displaystyle 5x^2y{\color{blue}(3x+2y)} + 15xy{\color{blue}(3x+2y)}(x-3y)$

The most obvious feature is the common factor $\displaystyle (3x + 2y)$

. . Factor it out: .$\displaystyle (3x+2y)\left[{\color{blue}5x^2y} + {\color{blue}15xy}(x - 3y)\right]$

We see that both terms contain $\displaystyle 5xy$

. . Factor it out: .$\displaystyle (3x + 2y)\cdot5xy[x + 3(x - 3y)] \;=\;(3x+2y)\cdot5xy[x + 3x - 9y]$

Final answer: .$\displaystyle 5xy(3x+2y)(4x - 9y)$

7. Thanks, that really helped seeing all the steps and following through with it. By chance is there anywhere on here to post homework with answers to see if its correct? I just wanna make sure I am doing everything right, because if I don't remember everything now. I am going to run into a whole lot of problems later with factoring.