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  1. #1
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    Homework Help

    What does 5(x)^2y(3x+2y)+15xy(3x+2y)(x-3y) factor out to?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by andy011789 View Post
    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?
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  3. #3
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    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
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by andy011789 View Post
    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:

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

    what else can we do here?
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  5. #5
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    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]
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  6. #6
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    Hello, Andy!

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

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



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

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


    We see that both terms contain 5xy

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


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

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  7. #7
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    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.
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