Timothy Gan
This is probably one of the most common mathematics mistakes we have done at least once in our life, which is (a+b)² = a²+b². Now what we need to understand is why is this not the case. Now before we start, we just have to understand the idea of a square. The concept of a square is pretty simple. Say if we want a², a² just means that we have a square of sides a. Thus, the area is multiplied by a. So, similarly for b².
What we need to understand is the length of this side here is b and this side here is b and hence the area here is b². So what does (a+b)² mean? This would mean that we have a huge square. Now in this case here, we're going to split one side into a and b and this side into a and b. This means that we have a side of a and this side will be b.
The whole side will just be a+b. And this will give us what we are looking for, which is an (a+b)². So in this case here, if you look at the big square here, we know that if we expand in this form [(a + b)² = a² + b²] we're actually missing out on something (Hint: purple colour in the diagram), right?
The area which we did not account for when we wrote such a common mistake is actually ab-ab right? So in other words, to fix the expansion, we need to just put 2ab in to get the correct expansion:
