What does 5(x)^2y(3x+2y)+15xy(3x+2y)(x-3y) factor out to?
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
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: .$\displaystyle 5xy(3x+2y)(4x - 9y)$
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.