What is the properties of difference of two squares?

The properties of the difference of two squares are:

1. The difference of two squares can be factored into the product of two binomials.
2. The factors of the difference of two squares are conjugates of each other.
3. The product of the sum and difference of two squares is equal to the difference of the squares of the two terms.
4. The difference of two squares is always a positive number or zero.

Properties of Difference of Two Squares:

1. Factorization:
```
a^2 - b^2 = (a + b)(a - b)
```

2. Expansion:
```
(a + b)(a - b) = a^2 - b^2
```

3. Quadratic Equation:
```
x^2 - a^2 = (x - a)(x + a)
```
This factorization helps solve quadratic equations of the form x^2 - a^2 = 0.

4. Difference of Cubes:
```
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
```
This is derived by expanding (a - b)(a^2 + ab + b^2) and using the difference of two squares factorization.

5. Sum of Cubes:
```
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
```
This is derived by expanding (a + b)(a^2 - ab + b^2) and using the difference of two squares factorization.

6. Conjugate Pairs:
For any real number a, (a + b)(a - b) is a conjugate pair. Conjugates have the same magnitude but opposite signs.

7. Product of Conjugates:
```
(a + b)(a - b) = a^2 - b^2
```
This is because the cross-multiplying terms cancel out.

8. Perfect Square Trinomials:
A trinomial of the form x^2 + 2ab + b^2 is a perfect square trinomial and can be factored as (x + b)^2.

9. Sum and Difference of Two Cubes:
```
a^3 ± b^3 = (a ± b)(a^2 ∓ ab + b^2)
```
This is derived by expanding (a ± b)(a^2 ∓ ab + b^2) and using the difference of two squares factorization.

10. Solving Quadratic Equations:
The difference of two squares can be used to solve quadratic equations that can be factored as (x - a)(x - b) = 0.