How would you do 7x squared + 27xy + 18y squared? I'm so used to the format of x squared + x + ___(insert number here)

 I  expect you want me to factorize it?

$$\\7x^2+ 27xy + 18y^2\\$$

This is a tough one.  

We want to find 2 numbers that mult to 7*18  and add to 27

prime factors of 7*18  are  7*3*3*2   I notice straight off that 21+6=27

so the numbers are  21 and 6

change 27xy into    21xy+6xy

$$\\7x^2+ 27xy + 18y^2\\ =7x^2+ 21xy +6xy+ 18y^2\\ =7x(x+3y)+6y(x+3y)\\ =(7x+6y)(x+3y)$$

Do you understand Anima ?