Question

Factorize y^4 - (x - y) ^4 ​

Answer 1

Step-by-step explanation:

Expression

=

x

4

−

y

4

Recall the factorization of the difference of two squares:

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

In our example, we will use this factorization twice.

Note:

x

4

=

(

x

2

)

2

and

y

4

=

(

y

2

)

2

Applying the factorization above:

Expression

=

(

x

2

+

y

2

)

(

x

2

−

y

2

)

Now, the second factor above is also the difference of two squares.

Hence, Expression

=

(

x

+

y

)

(

x

−

y

)

(

x

2

+

y

2

)

Answer 2

Step-by-step explanation:

${y}^{4} - (x - y)^{4} \\ = ({y}^{2})^{2} - ((x - y)^{2} )^{2} \\ = ({y}^{2} + (x - y)^{2})({y}^{2} - (x - y)^{2}) \\ = ({x}^{2} - 2xy + 2 {y}^{2} )( {x}^{2} + 2xy)$

HOPE....IT.....HELPS......U