Some two termed quadratic expressions are in the form of

**difference of two squares**. For example:x^{2}- 25 can be written as x^{2}- 5^{2}because 5^{2}equals 25

Some more examples:

- x
^{2}- 36 = x^{2}- 6^{2} - 9x
^{2}- 81 = (3x)^{2}- 9^{2} - 25x
^{2}- 36y^{2}= (5x)^{2}- (6y)^{2}

These quadratic expressions can be factored by applying the formula for difference of two squares:

For example, the quadratic expression x

x

For example, the algebraic expression (x + 2)(x - 2) can be expanded by distribution as follows:

(a^{2}- b^{2}) = (a + b)(a - b)

**Working forward with the formula - Factorization**For example, the quadratic expression x

^{2}- 36 can be written as x^{2}- 6^{2}.x

^{2}- 6^{2}can be compared to a^{2}- b^{2}in the above mentioned formula, hence you getx^{2}- 36 = x^{2}- 6^{2}= (x + 6)(x - 6)

**Working backward with the formula - Expansion**For example, the algebraic expression (x + 2)(x - 2) can be expanded by distribution as follows:

`(x + 2)(x - 2) = x^2 + 2x - 2x - 4 = x^2 - 4`.. which is the same result as obtained when applying the above formula backwards:

`(x + 2)(x - 2) = x^2 - 2^2 = x^2 - 4`