Question

Factorise : x to the power 4 - y to the power 4

Answer 1

 x4-y4 Final result : (x2 + y2) • (x + y) • (x - y) 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 by step solution :Step  1  :Trying to factor as a Difference of Squares :

 1.1      Factoring:  x4-y4 

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 :  x4  is the square of  x2 

Check :  y4  is the square of  y2 

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

Trying to factor as a Difference of Squares :

 1.2      Factoring:  x2 - y2 

Check :  x2  is the square of  x1 

Check :  y2  is the square of  y1 

Factorization is :       (x + y)  •  (x - y) 

Final result : (x2 + y2) • (x + y) • (x - y)

Answer 2

Answer:

Step-by-step explanation: