What is the right term to indicate the opposite of the math operation distribution?

I am studying math, and there's a term I don't know how to express, I just know that is the opposite of the operation of distribution of terms in an algebraic expression. For example, from the basic math operations we all learnt at primary school:

(a + b) * 3

... and if I distribute (distribution) the 3, I get:

3*a + 3*b

Now, what is the technical English name and verb for the reverse operation:

3(a + b)

?

• So far as I know, native speakers don't use "distribute" for that sense. You're expanding the formula, the opposite of which would probably be factorising (but I wouldn't be surprised to hear it called simplifying). Commented Jan 13, 2015 at 23:02
• @FumbleFingers You should write such as an answer. Your terms are what I learned, though it might have been factoring. Commented Jan 13, 2015 at 23:06
• I got A level maths, but that was a long time ago, and it's not like they would have actually taught us the appropriate words for the operations you're describing. Really I think this question should be migrated to math.se, but I'm prepared to be convinced otherwise. Commented Jan 13, 2015 at 23:06
• @fumblefingers i'm a native speaker and was taught "distribute" for this in school. anyone would know what you mean if you said "distribute the 3". Commented Jan 13, 2015 at 23:34
• @sgroves: Remember that factorising an expression simplifies it in some way. Factorising is the reverse of expanding brackets. I realise that's how we describe what we're doing to the whole equation, whereas OP here is asking what we're doing to a single term (in this case, the constant 3). But I speak English well and I'm better educated in matters mathematical than the average native speaker. If I don't know a word for this minutiae , I don't see how it's on topic for English language learners. Commented Jan 14, 2015 at 5:05

The word for this is "factoring". "Factor" can be used as a verb, just like "distribute". When you do this:

3*a + 3*b

3(a + b)

you are factoring out the 3. (Present tense: "factor out the three".) When you do this:

x^2 + 5x + 6 = (x + 2)(x + 3)

you are factoring the polynomial.

"Factor" is also a noun. When you do this

100 = 2 * 2 * 5 * 5

you are finding the prime factors of 100.

"Distribute" is mainly used as a verb. When you do this:

5(a + b) = 5*a + 5*b

You are distributing the 5. But you can't call the 5s "distributors" or anything like that.

The property of multiplication and addition that allows you to do all this is called the distributive property.

Formally, we would say factoring. Informally, in the U.S., you will often hear "pulling out."

x3y+2x2 = x2(xy+2) See what I did? I pulled out an ex squared.