Question 1015000
your expression is -5x^3 + x^9


since x^9 is equal to (x^3)^3, your expression becomes:


-5x^3 + (x^3)^3


you can now factor out a common (x^3) from the expression.


you will get:


-5x^3 + (x^3)^3 = x^3 * (-5 + (x^3)^2)


since -5 is equal to -1 * 5 and 1 * (x^3)^2 is equal to -1 * -1 * (x^3)^2, you can factor out a -1 to get:


x^3 * (-5 + (x^3)^2) is equal to:
x^3 * (-1 * 5 + -1 * -1 * (x^3)^2) which is equal to:
x^3 * (-1) * (5 + -1 * (x^3)^2) which is equal to:
x^3 * (-1) * (5 - (x^3)^2).
since (x^3)^2 is equal to x^6, your expression becomes equal to:
-x^3 * (5 - x^6)


your last expression became that way because:


-1 * x^3 is equal to -x^3
and:
(x^3)^2 is equal to x^(2*3) which is equal to x^6


x^9 became equal to (x^3)^3 because (x^3)^3 is equal to x^(3*3) which is equal to x^9.


so.....


you started with -5x^3 + x^9


and.....


you ended up with -x^3 * (5 - x^6)


you factored out a greatest common factor with a negative coefficient so the problem requirements have been satisfied.


you can confirm by applying the distributive law of multiplication to this final expression to get:


-x^3 * (5 - x^6) equals:
5 * (-x^3) - (x^6) * (-x^3) which is equal to:
-5x^3 + x^6 * x^3) which is equal to:
-5x^3 + x^(6+3) which is equal to:
-5x^3 + x^9 which looks exactly like your original expression.


an alternative way to check if you got it right is to give a random value to x and solve both the original expression and the final expression to see if they come up with the same answer.


the original expression is -5x^3 + x^9


the final expression is -x^3 * (5 - x^6)


when x = 17 (chosen at random), the original expression is equal to 1.185878519 * 10^11 and the final expression is equal to 1.185878519 * 10^11.


they're the same, so the final expression is equivalent to the original expression.