There is a useful formula that can often help us to simplify algebraic expression and to solve algebraic equations. It is called the difference of two squares formula, and is specified below. Copy it down and memorise it.

As is typically the case in mathematics, this algebraic equation reflects a geometrical fact. The diagram below helps to demonstrate this.

We can make some numerical questions easier, either by expanding brackets, or by using the difference of two squares formula.

For instance, suppose that we want to find 54².

We can write this as (50+4)². Then by expanding brackets we see that this is the same as 50²+2x50x4+4². This gives us an easier way of calculating it.

Using the difference of two squares formula, we can find and easier way to calculate 103 x 97 for instance. We can also find an easier way to calculate 21² – 19² (for instance).

Exercise

Let’s complete exercise 19C on page 311 of the textbook:

The answers are below:

Now let’s use the formula to change the form of some algebraic problems.

Example

Exercise

Let’s complete exercise 19D from page 312 of the textbook:

The answers are below: