How to simplify equations with a constant times a polynomial to a powerI've started doing integration in class and I often come across parts like this towards the end of my integration: 2 ( 6 x 2 + 6 x + 9 ) 3 / 2 3 + CAnd I get stuck. How should I go about simplifying these? Do I distribute the two and then try to do something with the exponent, or am I not allowed to because the polynomial is being raised to a power?All help is appreciated, I am really stuck because almost all of my problems end up in this form at some point or another.

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How to simplify equations with a constant times a polynomial to a powerI&#039;ve started doing integration in class and I often come across parts like this towards the end of my integration:            2      (      6              x        2            +      6      x      +      9              )                  3                      /                    2                      3    +  CAnd I get stuck. How should I go about simplifying these? Do I distribute the two and then try to do something with the exponent, or am I not allowed to because the polynomial is being raised to a power?All help is appreciated, I am really stuck because almost all of my problems end up in this form at some point or another.

enfujahl · Accepted Answer

This looks like it&#039;s in simplest form. You could check to see whether the inner polynomial factors nicely, but this one doesn&#039;t. All the coefficients of the polynomial are divisible by   3, but it only makes things messier to pull out       3          3              /            2      Incidentally, supposing the polynomial factored, you have to be careful when simplifying. For instance, if we make it       x    2   instead of   6      x    2  , then:                    (                  x          2                +        6        x        +        9                  )                      3                          /                        2                                              =                              (            (            x            +            3                          )              2                        )                                3                          /                        2                                                            =                  |                x        +        3                              |                    3                                                      (not                           (              x              +              3                              )                3                                      !)

How to simplify equations with a constant times a polynomial to a powerI've started doing...

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