Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "d2"   was replaced by   "d^2".  2 more similar replacement(s).

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  a²b²-d² 

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 :  a²  is the square of  a¹ 

Check :  b²  is the square of  b¹ 

Check :  d²  is the square of  d¹ 

Factorization is :       (ab + d)  •  (ab - d) 

Final result :

  (ab + d) • (ab - d)