Question 257890
expression is:


{{{2*x*((5*x^2-3*x+2)-(6*x^3+6*x^2)/(3*x^2))}}}


you process operations within parentheses first starting from the inner parentheses and working to the outer parentheses.


your expressions within the inner parentheses can't be processed any further.


they are:


{{{(5*x^2-3*x+2)}}} and {{{(6*x^3+6*x^2)}}} and {{{(3*x^2)}}}


your terms in the outer parentheses need to be processed next.


they are:


{{{((5*x^2-3*x+2)-(6*x^3+6*x^2)/(3*x^2))}}}


you would need to divide {{{(6*x^3+6*x^2)}}} by {{{(3*x^2)}}} first.


that gets you {{{(2*x + 2)}}}


the expression within the outer parenthese becomes:


{{{((5*x^2-3*x+2) - (2*x + 2))}}}


you process this next by removing the inner parentheses from the outer parentheses to get:


{{{(5*x^2 - 3*x + 2 - 2*x - 2))}}} which becomes:


{{{(5*x^2 - 5*x)}}}


you replace the original expression within the outer parentheses by this to make your original equation of:


{{{2*x*((5*x^2-3*x+2)-(6*x^3+6*x^2)/(3*x^2))}}} becomes:


{{{2*x*(5*x^2 - 5*x)}}}


you multiply each term within the parentheses by 2*x to get:


{{{10*x^3 - 10*x^2}}}


if you did this right, then you should be able to get the same results in the original equation and the final equation for any value of x.


take x = 5


final equation of {{{10*x^3 - 10*x^2}}} becomes:


{{{10*5^3 - 10*5^2 = 1000}}}


original equation of {{{2*x*((5*x^2-3*x+2)-(6*x^3+6*x^2)/(3*x^2))}}} becomes:


{{{2*5*((5*5^2 - 3*5 + 2) - (6*5^3 + 6*5^2)/(3*5^2))}}} which becomes:


{{{10 * ((125 - 15 + 2) - (750 + 150)/75)}}} which becomes:


{{{10 * ((112) - (900/75))}}} which becomes:


{{{10 * 100}}} which becomes:


1000


since they both come up with the same answer, the final equation is equivalent to the original equation which indicates we simplified the equation properly.


the simplified equation is:


{{{10*x^3 - 10*x^2}}}