Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2a2 -  (a5))2

Step  2  :

Step  3  :

Pulling out like terms :

 3.1    Simplify ( 2a²-a⁵ )²

Put the exponent aside and simplfy the base by pulling out like factors :
 2a²-a⁵  =  -a² • (a³-2) 

Remember the 4th law of exponents : (a • b)^m= a^m• b^m

Retract the exponent and apply the 4th law to the simplified base: ( -a² • (a³-2) )² =  (-a²)² • (a³-2)²  

Trying to factor as a Difference of Cubes:

 3.2      Factoring:  a³-2 

Put the exponent aside, try to factor  a³-2 

Theory : A difference 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 :

 3.3    Find roots (zeroes) of :       F(a) = (a³-2)²
Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  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  1  and the Trailing Constant is  -2.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  (-a2)2 • (a3 - 2)2