 how to multiply two binomials. What is 2x plus 3 times 5x plus 4? It might help us to consider the product 2 plus 3 times 5 plus 4. Obviously this is just a decomposition of 5 into 2 plus 3, and this is a decomposition of 9 into 5 plus 4, so this is just 5 times 9, which is 45. How can we use that to help us understand how to multiply two binomials? Another way of multiplying these numbers, notice that these are also binomials. They are not simplified, and they are constants, but they are binomials. If we multiply 2 times 5, and we add to that 2 times 4, and we add to that 3 times 5, and 3 times 4, we get 10 plus 8 plus 15 plus 12, which is equal to 45. So let us follow the same steps. This first term times this term, that is equal to 10x squared. This term by the second term here, that is 8x. This term by this guy, that is 15x. And this guy by this guy, that is 12. So this is equal to 10x squared plus 23x plus 12. And now we see that the multiplication of 2 binomials is something that is not so strange after all. It is something that we can do with integers or with any other numbers. It is just a property of numbers. We decompose them and we multiply them in that way. So now it doesn't seem as an arcane method of multiplying these 2 objects, but as something that is very natural.