How do I add like terms?

Question

In a math problem, I had to simplify by combining terms. My questions was (3y+1)(-2)+y
In the end I got the wrong answer. I want to know:
(why) can I multiply the coefficient, 3, with -2 to get -6, even though -2 isn't followed by a y?
Please explain, I'm so confused.

Answer 1

When you multiply 3y by -2, you get -6y. You can multiply them, but you have to keep the variable y. Then multiply 1 by -2, which is -2. Now you have -6y-2+y, which gives you -5y-2. Hope that helps. =)

Answer 2

(3y+1)(-2)+y

-2 is a constant that you can distribute to the numbers in the parentheses. The distributive property is something most of us learn around 4th or 5th grade.

(3y+1)(-2) +y
First do the multiplication part.
(3y+1)(-2)+y --> -2(3Y)+(1)(-2)
=-6Y -2 +y
-6Y plus Y will be -5Y

-5Y - 2 Should be your answer.

Answer 3

Because they're like terms! :-]

Okay, imagine each variable as a different colored marble. The y's are red marbles and the numbers are blue marbles. You can't add (or in this case, multiply) a red and a blue marble together, but you can add a red and red OR blue and blue, right?

Hope it makes a bit more sense now.