Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a4"   was replaced by   "a^4". 

Step  1  :

Equation at the end of step  1  :

  (a2) -  22a4
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   a² - 4a⁴  =   -a² • (4a² - 1) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  4a² - 1 

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 :  4  is the square of  2 
Check : 1 is the square of 1
Check :  a²  is the square of  a¹ 

Factorization is :       (2a + 1)  •  (2a - 1) 

Final result :

  -a2 • (2a + 1) • (2a - 1)