Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  72h4 -  16

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  49h⁴-16 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  49  is the square of  7 
Check : 16 is the square of 4
Check :  h⁴  is the square of  h² 

Factorization is :       (7h² + 4)  •  (7h² - 4) 

Polynomial Roots Calculator :

 2.2    Find roots (zeroes) of :       F(h) = 7h² + 4
Polynomial Roots Calculator is a set of methods aimed at finding values of  h  for which   F(h)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  h  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  7  and the Trailing Constant is  4.

 The factor(s) are:

of the Leading Coefficient :  1,7
 of the Trailing Constant :  1 ,2 ,4

 Let us test ....

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares :

 2.3      Factoring:  7h² - 4 

Check :  7  is not a square !!

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

Final result :

  (7h2 + 4) • (7h2 - 4)