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

Math
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
Factor using the perfect square rule.
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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

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