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

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- Sep 30th 2007, 12:26 PMandy011789Homework Help
What does 5(x)^2y(3x+2y)+15xy(3x+2y)(x-3y) factor out to?

- Sep 30th 2007, 12:29 PMJhevon
- Sep 30th 2007, 12:35 PMandy011789Common 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

- Sep 30th 2007, 12:40 PMJhevon
- Sep 30th 2007, 12:45 PMandy011789
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]

- Sep 30th 2007, 12:46 PMSoroban
Hello, Andy!

Quote:

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

- Sep 30th 2007, 12:56 PMandy011789
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.