What we have is known as a binomial expression. It's called an "expression" because there is no equal sign. If there was it would be called an equation. But for now we'll just solve the expression part.
There is a couple of ways of doing this. We can do it by multiplying the two binomials together using distribution or using the FOIL technique (which I personally prefer).
FOIL stands for F-first, O-outside, I-inside, L-last. We will multiply together each of these terms, after all this is a multiplication problem, combine like terms, and, viola, the expression is multiplied and simplified.
First: 3w x 4w = 12w^2
Outside: 3w x -5 = -15w
Inside: -3 x 4w = -12w
Last: -3 x -5 = 15
So what we end up with is 12w^2 - 15w - -12w + 15
Combine like terms, which in this case are only the terms ending in "w" and we get:
12w^2 - 3w + 15 Factor by a least common demonator of 3 and we get 3(4w^2-w + 5)
