how do you factor x^2+29xy+100y^2

Answer 1

Use the quadratic equation, with a = 1, b = 29 y and c = 100y^2. This will give you two roots that will have "y" in them. Call them y1 and y2.

The factors will be (x-y1)(x-y2)

Answer 2

you know your factors must look like
(x + ?y)(x + ?y)
what two numbers add to 29 and multiply to get 100 ?
how about 25 and 4
so
(x+25y)(x+4y)