How do you factor 15x^2 + 8xy + y^2 ?

have a look at the factors of 15

as said, factors of 15 are 1,3,5

and you see that 3+5=8 (middle factor coefficient)

so 15x^2 + 8xy + y^2 = (3x+y)(5x+y)

The answer was found to be two factors: (3x+y)(5x+y) .

Here is the proof that (3x+y)(5x+y) is correct.

Use FOIL to return to the original polynomial expression. This is how to check for the right answer.

(3x+y)(5x+y) = original polynomial expression

3x * 5x = 15x^2
3xy + 5xy = 8xy
y * y = y^2

Now put it all together.

15x^2 + 8xy + y^2 = original polynomial expression

It checks! We now know for sure that (3x+y)(5x+y) is the corrected factored form of your original polynomial expression.