<PRE><B>Question 367621</B>
the problem is:


9 * (2x + 1)^3 + 6 * (2x+1)^2 - 15 * (2x+1)


(2x+1)^2 is equal to 4x^2 + 4x + 1


(2x+1)^3 is equal to 8x^3 + 12x^2 + 6x + 1


9 * (2x+1)^3 is equal to 72x^3 + 108x^2 + 54x + 9


6 * (2x+1)^2 is equal to 24x^2 + 24x + 6


15 * (2x + 1) is equal to 30x + 15


your expression becomes:


72x^3 + 108x^2 + 54x + 9 + 24x^2 + 24x + 6 - (30x + 15)


remove parentheses to get:


72x^3 + 108x^2 + 54x + 9 + 24x^2 + 24x + 6 - 30x - 15


bring your like terms together to get:


72x^3 + 108x^2 + 24x^2 + 54x + 24x - 30x + 9 + 6 - 15


combine like terms to get:


72x^3 + 132x^2 + 48x


this is your original answer after you have multiplied all factors together.


you can factor out an x to get:


x * (72x^2 + 132x + 48)


you can factor out a 12 to get:


12 * x * (6x^2 + 11x + 4)


6x^2 + 11x + 4 factors out to be (2x+1) * (3x + 4) because when you multiply those factors together, you get 6x^2 + 11x + 4.


your solution is therefore equal to:


12 * x * (2x + 1) * (3x + 4)


if you multiply all of those together, you will get back to your original equation of 72x^3 + 132x^2 + 48x which was derived by multiplying all the original factors together.



 


</PRE>