 How to square a binomial? What is 3x plus 5 that binomial squared? Let us consider first the product 3 plus 5 squared. Yes, this is the same technique we applied to multiply any two binomials. But let us see it again in this context. This is the eight decomposition of 8 and that's 8 squared which is just 64. But we can also see that by definition the square of a number is just that number times itself and we can distribute like we did in the other video 3 times 3 plus 3 times 5 plus 5 times 3 plus 5 times 5. And this is just 9 plus 15 plus 15 plus 25 which you can readily see is 64. So let us use that here. When we square this binomial it's just the binomial times itself. Now we distribute the terms 3 times 3x times 3x is 9x squared, 3x times 5 is 15x, this times this is 15x and this times this is 25. We combine like terms and we have that this is 9x squared plus 30x plus 25. Some people ask me why don't you just teach the foil method? You know where you first multiply the the first terms then the outside terms and the inside terms and then the last terms. Well because that only works from one particular case when you're multiplying binomials. You have to memorize it you're not understanding much and then worst of all you cannot extend it to multiplication of other polynomials and that's basically why I prefer to teach it this way through integer decomposition. You see a construction something that you do understand you know addition of integers you know subtraction of integers and you learn. Thank you.