Idk how to do this so when u get the answer show me how to do it

according to: https://www.tiger-algebra.com/drill/41u2-(-2u8)/

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "u8"   was replaced by   "u^8".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 (41 • (u2)) -  (0 -  2u8)

STEP  

2

:

Equation at the end of step

2

:

 41u2 -   -2u8

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  2u8 + 41u2  =   u2 • (2u6 + 41)  

Trying to factor as a Sum of Cubes:

4.2      Factoring:  2u6 + 41  

Theory : A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a2-ab+b2)

Proof  : (a+b) • (a2-ab+b2) =

   a3-a2b+ab2+ba2-b2a+b3 =

   a3+(a2b-ba2)+(ab2-b2a)+b3=

   a3+0+0+b3=

   a3+b3

Check :  2  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

4.3    Find roots (zeroes) of :       F(u) = 2u6 + 41

Polynomial Roots Calculator is a set of methods aimed at finding values of  u  for which   F(u)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  u  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  41.

The factor(s) are:

of the Leading Coefficient :  1,2

of the Trailing Constant :  1 ,41

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        43.00      

     -1       2        -0.50        41.03      

     -41       1       -41.00       9500208523.00      

     -41       2       -20.50       148440798.53      

     1       1        1.00        43.00      

     1       2        0.50        41.03      

     41       1        41.00       9500208523.00      

     41       2        20.50       148440798.53      

Polynomial Roots Calculator found no rational roots

Final result :

 u2 • (2u6 + 41)