Question

factorise the expression x⁴-y⁴​​

Answer 1

Answer:

(x2 + y2) • (x + y) • (x - y)

Step-by-step explanation:

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

Step-by-step explanation:

given=x⁴-y⁴

(x²)²-(y²)²

algebraic identity =a²-b²=(a+b) (a-b)

(ײ+y²) (x²-y²)

=(x+y ) (x-y)

i hope that it will help u