1. Problem: Factorise the following expression using the cross method: $d(d - 5) - 84$. 2. Expand to standard quadratic form. $$d(d - 5) - 84 = d^2 - 5d - 84$$ 3. Formula and rules: For a quadratic $ax^2+bx+c$ find two integers that multiply to $a c$ and add to $b$. 4. Since $a=1$ here, we need two integers that multiply to $-84$ and add to $-5$. 5. Search for factor pairs; try $(-12,7)$ because they satisfy: $$-12+7=-5,\quad -12\times 7=-84$$ 6. Therefore factorise the quadratic as: $$d^2 - 5d - 84 = (d - 12)(d + 7)$$ 7. Final answer: Answer for blank 1: $(d - 12)(d + 7)$.