Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have

$$(2a + 1)(2b + 1)$$

which apparently expands to

$$4ab + 2a + 2b + 1$$

and then can be written as

$$2(2ab + a + b) + 1 \,.$$

From where did we get the $4ab$ term?

share|cite|improve this question
up vote 3 down vote accepted

For this, an application of the distributive law gives us that for any $a,b,c,d \in \mathbb{R}$ that $(a + b)(c + d) = (ac + db + bc + bd)$. In this case we would then have, $$(2a + 1)(2b + 1) = (2a)(2b) + (1)(2a) + (1)(2b) + (1)(1) = 4ab + 2a + 2b +1$$ as desired.

share|cite|improve this answer

Each term in the first set of brackets is multiplied by each term in the second set of brackets. So the "2a" in the first set of brackets is multiplied by "2b" in the second set of brackets: 2a multiplied by 2b = 4ab

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.