1. **State the problem:** Factor the expressions $t^2 - 49$ and $t^2 - 14t + 49$. 2. **Recall formulas:** - Difference of squares: $a^2 - b^2 = (a - b)(a + b)$. - Perfect square trinomial: $a^2 - 2ab + b^2 = (a - b)^2$. 3. **Factor $t^2 - 49$:** - Recognize $49 = 7^2$. - Apply difference of squares: $$t^2 - 49 = (t - 7)(t + 7)$$ 4. **Factor $t^2 - 14t + 49$:** - Recognize $14t = 2 \times 7 \times t$ and $49 = 7^2$. - Apply perfect square trinomial formula: $$t^2 - 14t + 49 = (t - 7)^2$$ **Final answers:** - $t^2 - 49 = (t - 7)(t + 7)$ - $t^2 - 14t + 49 = (t - 7)^2$