8.7 Factoring Special Cases

Notes

Look for these patterns:

• Difference of squares: $a^2 - b^2 = (a + b)(a - b)$. Example: $x^2 - 36 = (x + 6)(x - 6)$.
• Perfect square trinomials: $a^2 + 2ab + b^2 = (a + b)^2$ and $a^2 - 2ab + b^2 = (a - b)^2$.
• A sum of squares like $x^2 + 9$ does not factor over the real numbers.
• Factor completely: $2x^2 - 50 = 2(x^2 - 25) = 2(x + 5)(x - 5)$.