Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y4"   was replaced by   "y^4".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (64 • (x4)) -  (22•32y4)
 Step  2  :

Equation at the end of step  2  :

  26x4 -  (22•32y4)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   64x⁴ - 36y⁴  =   4 • (16x⁴ - 9y⁴) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  16x⁴ - 9y⁴ 

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 :  16  is the square of  4 
Check : 9 is the square of 3
Check :  x⁴  is the square of  x² 

Check :  y⁴  is the square of  y² 

Factorization is :       (4x² + 3y²)  •  (4x² - 3y²) 

Trying to factor as a Difference of Squares :

 4.3      Factoring:  4x² - 3y² 

Check :  4  is the square of  2 
Check : 3 is not a square !!

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

Final result :

  4 • (4x2 + 3y2) • (4x2 - 3y2)