• Some expressions have special forms that can be factored directly without searching for two numbers.
• The first such form is the difference of two squares:

a² − b² = (a − b)(a + b)

• Both terms must be perfect squares, and the minus sign between them identifies the pattern.
• For example, x² − 49 = x² − 7² = (x − 7)(x + 7).
• The check by multiplication works because the two middle terms cancel each other.
• Note a sum of two squares, such as x² + 9, does not factor into real factors, because it is not in the form of a difference of two squares.
• Special forms are also useful for quick calculation.
• For example, 512 − 492 = (51 − 49)(51 + 49) = 2 × 100 = 200.
• Check: 2601 − 2401 = 200.