factorise x^4+x^2y^2+y^4

To factorize the expression x^4 + x^2y^2 + y^4, we can use the factoring formula for the sum of cubes.

Step 1: Rewrite the expression as (x^4 + 2x^2y^2 + y^4) - x^2y^2.

Step 2: Notice that (x^2 + y^2)^2 = x^4 + 2x^2y^2 + y^4.

Step 3: Substitute this into the expression to get (x^2 + y^2)^2 - x^2y^2.

Step 4: Now, we have a difference of squares. Recall that a^2 - b^2 = (a + b)(a - b).

Step 5: Apply the difference of squares formula to get ((x^2 + y^2) + xy)((x^2 + y^2) - xy).

Therefore, the expression x^4 + x^2y^2 + y^4 can be factorized as ((x^2 + y^2) + xy)((x^2 + y^2) - xy).