# Y9. Algebra. Quadratic Equations. Difference between Two Squares

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: