Expanding brackets part three

Here is a depiction of

The sides of the outer square are . The area of the outer square represents We can see this is made up of the red square and the two yellow 5 rectangles and the blue square.

We can rearrange these shapes to show this more clearly. gives

We can generalise this. When we expand brackets that have the form where c is a constant, we get

Going back to our example, when the constant is 5, we get

You should be able to look at similar brackets that are squared and be able to quickly see what the terms expand to.

For example

You may even get to the stage where you can look at some squared bracketed term like and see straight away that this is the same as