Solve Other Factorizations (a4-b4)/(a-b) Tiger Algebra Solver

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): “b4”   was replaced by   “b^4”.  1 more similar replacement(s).

Step

 1 

:

            a4 - b4
 Simplify   ———————
             a - b 

Trying to factor as a Difference of Squares :

 1.1      Factoring:  a4 – b4 

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 :  a4  is the square of  a2 

Check :  b4  is the square of  b2 

Factorization is :       (a2 + b2)  •  (a2 – b2) 

Trying to factor as a Difference of Squares :

 1.2      Factoring:  a2 – b2 

Check :  a2  is the square of  a1 

Check :  b2  is the square of  b1 

Factorization is :       (a + b)  •  (a – b) 

Canceling Out :

 1.3    Cancel out  (a – b)  which appears on both sides of the fraction line.

Final result :

  (a2 + b2) • (a + b)