1. **State the problem:** Fully factorise the quadratic expression $t^2 + 7t - 18$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Apply to our problem:** Here, $a=1$, $b=7$, and $c=-18$. We need two numbers that multiply to $1 \times (-18) = -18$ and add to $7$. 4. **Find the numbers:** The pair is $9$ and $-2$ because $9 \times (-2) = -18$ and $9 + (-2) = 7$. 5. **Rewrite the middle term:** $$t^2 + 9t - 2t - 18$$ 6. **Group and factor:** $$ (t^2 + 9t) - (2t + 18) = t(t + 9) - 2(t + 9) $$ 7. **Factor out the common binomial:** $$ (t - 2)(t + 9) $$ **Final answer:** The fully factorised form is $$(t - 2)(t + 9)$$.