The equations shown are quadratic expressions in the form $x^2 - a^2$, where each can be factored using the difference of squares formula:

$x^2 - a^2 = (x - a)(x + a)$

Let's apply this rule to each of the given quadratics:

1. $x^2 - 16$ $16 = 4^2 \quad \Rightarrow \quad x^2 - 16 = (x - 4)(x + 4)$

2. $x^2 - 36$ $36 = 6^2 \quad \Rightarrow \quad x^2 - 36 = (x - 6)(x + 6)$

3. $x^2 - 121$ $121 = 11^2 \quad \Rightarrow \quad x^2 - 121 = (x - 11)(x + 11)$

4. $x^2 - 196$ $196 = 14^2 \quad \Rightarrow \quad x^2 - 196 = (x - 14)(x + 14)$

Final answers:

1. $x^2 - 16 = (x - 4)(x + 4)$
2. $x^2 - 36 = (x - 6)(x + 6)$
3. $x^2 - 121 = (x - 11)(x + 11)$
4. $x^2 - 196 = (x - 14)(x + 14)$

Let me know if you need further details!

Related Questions:

1. How can we apply the difference of squares to higher degree polynomials?
2. What other factoring methods are there for quadratics?
3. Can the difference of squares formula be used for cubic terms?
4. What is the general process for factoring expressions involving multiple variables?
5. How can we identify when a quadratic can be factored using the difference of squares?

Tip: Always check if the quadratic expression can be written as a difference of squares before applying the formula.