Question

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Answer 1

Answer:

(x2 + y2) • (x + y)

Step-by-step explanation:

Step  1  :

           x4 - y4

      ———————

            x - y  

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)  

Canceling Out :

1.3    Cancel out  (x - y)  which appears on both sides of the fraction line.

Final result :

 (x2 + y2) • (x + y)

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Answer 2

Answer:x3+x2y+y2x+y3

Step-by-step Explanation=

Look at the following image