# Sunday Maths: Simplifying Squares

This is a simple method to make it easier to calculate squares in your head (or on paper). The key is the following equation:

```x² = (x+y)(x-y) + y²
```

If we multiply the terms in parenthesis you can see how these are equal:

```x² = (x+y)(x-y) + y²
x² = x² +yx -yx -y² +y²
x² = x²
```

We can use this to simplify the calculation of any x² by choosing a value of y such that (x-y)(x+y) becomes easy to calculate. For example:

```99² = ?
Using y = 1
99² = (99-1)(99+1) + 1²
99² = (98)(100) + 1
99² = 9800 + 1
99² = 9801
```

This technique works best when x is close to a power of 10, such as the above example. In more difficult cases it may be necessary to apply this technique recursively to calculate y² as well:

```72² = ?
Using y = 22
72² = (72-22)(72+22) + 22²
72² = (50)(94)       + (22+2)(22-2) + 2²
72² = 9400 ÷ 2       + (24)(20)     + 2²
72² = 4700           + 480          + 4
72² = 5184
```

Note also the use of 50=100÷2 to simplify the calculation of 50×94.