Write an expression equivalent to two 𝑎 plus two 𝑏.
Two 𝑎 and two 𝑏 are unlike terms because one has an 𝑎 and one has a 𝑏, which means we cannot combine them. However, they do have something in common. They have a two in common. This will be considered a greatest common factor. The largest number we can take out of each term two. And sometimes, we simplify that by saying the GCF.
So we take out the two. And if we would take out a two from two 𝑎, essentially taking two 𝑎 and dividing by two, we would be left with 𝑎. And then, the same thing for 𝑏, you take out a two and you’re left with 𝑏.
Now, we need to make sure we used the correct sign. And since it’s a plus, we need 𝑎 plus 𝑏. Therefore, an expression that is equivalent to two 𝑎 plus two 𝑏 would be two times 𝑎 plus 𝑏. This is like using the distributive property backwards.