Answer:
(3x + 4y)(x + 2y)
Explanation:
3x^2+ 10xy + 8y^2
All signs are positive, so we'll only look at positive factors of 3 and 8.
3 factors into 3 and 1.
8 factors into 4 and 2, and it also factors into 8 and 1.
I like to try closer factors in value, so I'll start with 4 and 2 for 8.
Try:
(3x + 2y)(x + 4y) = 3x^2 + 12xy + 2xy + 8y^2 = 3x^2 + 14xy + 8y^2
The middle term does not work. Switch 2y and 4y and try again.
Try:
(3x + 4y)(x + 2y) = 3x^2 + 6xy + 4xy + 8y^2 = 3x^2 + 10xy + 8y^2
It works.
Answer: (3x + 4y)(x + 2y)