25x2y2+60xy+36

Rewrite x2y2 as (xy)2.

25(xy)2+60(xy)+36

Let u=xy. Substitute u for all occurrences of xy.

25u2+60u+36

Rewrite 25u2 as (5u)2.

(5u)2+60u+36

Rewrite 36 as 62.

(5u)2+60u+62

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅(5u)⋅6

Simplify.

2ab=60u

Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=5u and b=6.

(5u+6)2

(5u+6)2

Replace all occurrences of u with xy.

(5(xy)+6)2

Remove parentheses.

(5xy+6)2

Factor 25x^2y^2+60xy+36