document.write( "Question 1038091: Hello, I am having a really hard time finding the factors of these. It would be much appreciated for you to answer :)\r
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Algebra.Com's Answer #652807 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "15x^3(x+y)^2 - 30x^2(x+y) - 45x(x+y)^4\r\n" );
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document.write( "15             30           45 \r\n" );
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document.write( "Look at the numbers: 15, 30, 45\r\n" );
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document.write( "What is the largest integer that will divide evenly \r\n" );
document.write( "into all three of those numbers?  It's 15.  So 15 is \r\n" );
document.write( "a common factor that can be factored out.\r\n" );
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document.write( "So we know the factoring starts like this:\r\n" );
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document.write( "15      [                        ]\r\n" );
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document.write( "Next we look at the powers of x: x^3, x^2, x^4\r\n" );
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document.write( "15x^3(x+y)^2 - 30x^2(x+y) - 45x(x+y)^4\r\n" );
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document.write( "  x^3            x^2          x \r\n" );
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document.write( "What is the largest power of x that will divide evenly into \r\n" );
document.write( "all three of those?  x means x^1.  The largest power of x\r\n" );
document.write( "that will divide evenly into all three of those is x^1 or just\r\n" );
document.write( "x, the smallest power of x.  So we can factor out x. So the \r\n" );
document.write( "factoring will look like this:\r\n" );
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document.write( "15x     [                        ]\r\n" );
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document.write( "Next we look at (x+y)^2, (x+y), and (x+y)^4\r\n" );
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document.write( "Next we look at the powers of x: x^3, x^2, x^4\r\n" );
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document.write( "15x^3(x+y)^2 - 30x^2(x+y) - 45x(x+y)^4\r\n" );
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document.write( "     (x+y)^2        (x+y)      (x+y)^4\r\n" );
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document.write( "What is the largest power of (x+y) that will divide evenly into \r\n" );
document.write( "all three of those?  (x+y) means (x+y)^1.  The largest power of \r\n" );
document.write( "(x+y) that will divide evenly into all three of those is (x+y)^1 \r\n" );
document.write( "or just (x+y), the smallest power of (x+y).  So we can factor out \r\n" );
document.write( "(x+y). So the factoring will look like this:\r\n" );
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document.write( "15x(x+y)[                        ]\r\n" );
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document.write( "The first term of the original expression is 15x^3(x+y)^2.\r\n" );
document.write( "What factors does 15x^3(x+y)^2 have that 15x(x+y) does NOT\r\n" );
document.write( "have? 15x^3(x+y)^2 has factors x^2 and (x+y) that 15x(x+y)\r\n" );
document.write( "does not have, because x needs to be multiplied by x^2 to\r\n" );
document.write( "get x^3 and (x+y) needs to be multiplied by itself (x+y) to\r\n" );
document.write( "get (x+y)^2.  So the first term to put inside the brackets\r\n" );
document.write( "is x^2(x+y) \r\n" );
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document.write( "15x(x+y)[x^2(x+y)                ]\r\n" );
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document.write( "The second term of the original expression is - 30x^2(x+y).\r\n" );
document.write( "What factors does - 30x^2(x+y) have that 15x(x+y) does NOT\r\n" );
document.write( "have? - 30x^2(x+y) has only factors -2 and x that 15x(x+y)\r\n" );
document.write( "does not have, because 15 needs to be multiplied by -2 to\r\n" );
document.write( "get -30 and x needs to be multiplied by itself x to\r\n" );
document.write( "get x^2.  So the second term to put inside the brackets\r\n" );
document.write( "is - 2x.  So now we have \r\n" );
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document.write( "15x(x+y)[x^2(x+y) - 2x           ]\r\n" );
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document.write( "The third and final term of the original expression is - 45x(x+y)^4.\r\n" );
document.write( "What factors does - 45x(x+y)^4 have that 15x(x+y) does NOT\r\n" );
document.write( "have? - 45x(x+y)^4 has factors -3 and (x+y)^3\r\n" );
document.write( "does not have, because 15 needs to be multiplied by -3 to\r\n" );
document.write( "get -45 and (x+y) needs to be multiplied by (x+y)^2 to\r\n" );
document.write( "get (x+y)^3.  So the third term to put inside the brackets\r\n" );
document.write( "is - 2(x+y)^2.  So now we have \r\n" );
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document.write( "15x(x+y)[x^2(x+y) - 2x - 3(x+y)^3]\r\n" );
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document.write( "Now we have to remove the parentheses within the brackets:\r\n" );
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document.write( "15x(x+y)[x^3 + x^2y - 2x - 3(x+y)(x+y)(x+y)]\r\n" );
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document.write( "15x(x+y)[x^3 + x^2y - 2x - 3(x+y)(x^2+2xy+y^2)]\r\n" );
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document.write( "15x(x+y)[x^3 + x^2y - 2x - 3(x^3+2x^2y+xy^2+x^2y+2xy^2+y^3)]\r\n" );
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document.write( "15x(x+y)[x^3 + x^2y - 2x - 3(x^3+3x^2y+3xy^2+y^3)]\r\n" );
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document.write( "15x(x+y)[x^3 + x^2y - 2x - 3x^3 - 9x^2y - 9xy^2 - 3y^3]\r\n" );
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document.write( "15x(x+y)[-2x^3 - 8x^2y - 9x^2y - 2x - 3y^3]\r\n" );
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document.write( "Since all those terms are negative we can take a negative sign\r\n" );
document.write( "out front:\r\n" );
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document.write( "-15x(x+y)[2x^3 + 8x^2y + 9xy^2 + 2x + 3y^3]\r\n" );
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document.write( "We can only change the brackets to parentheses\r\n" );
document.write( "because they no longer hold parentheses:\r\n" );
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document.write( "-15x(x+y)(2x^3 + 8x^2y + 9xy^2 + 2x + 3y^3)\r\n" );
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document.write( "Edwin
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