1. **Problem:** Factorise the algebraic expressions given. 2. **Formula/Rule:** To factorise expressions, look for common factors or use grouping methods. 3. **(a) Factorise $pq - qr - pw + rw$:** Group terms: $(pq - pw) + (-qr + rw)$ Factor each group: $p(q - w) - r(q - w)$ Factor out common binomial: $(q - w)(p - r)$ 4. **(b) Factorise $x^2 + xy + 6x + 6y$:** Group terms: $(x^2 + xy) + (6x + 6y)$ Factor each group: $x(x + y) + 6(x + y)$ Factor out common binomial: $(x + y)(x + 6)$ 5. **(c) Factorise $3ab - 9ad + bc - 3cd$:** Group terms: $(3ab - 9ad) + (bc - 3cd)$ Factor each group: $3a(b - 3d) + c(b - 3d)$ Factor out common binomial: $(b - 3d)(3a + c)$ 6. **(d) Factorise $ah + aj - bh - bj$:** Group terms: $(ah + aj) - (bh + bj)$ Factor each group: $a(h + j) - b(h + j)$ Factor out common binomial: $(h + j)(a - b)$ 7. **(e) Factorise $jm - jn + ym - yn$:** Group terms: $(jm - jn) + (ym - yn)$ Factor each group: $j(m - n) + y(m - n)$ Factor out common binomial: $(m - n)(j + y)$ 8. **(f) Factorise $9xy - 3xz + 12py - 4pz$:** Group terms: $(9xy - 3xz) + (12py - 4pz)$ Factor each group: $3x(3y - z) + 4p(3y - z)$ Factor out common binomial: $(3y - z)(3x + 4p)$ **Final answers:** (a) $(q - w)(p - r)$ (b) $(x + y)(x + 6)$ (c) $(b - 3d)(3a + c)$ (d) $(h + j)(a - b)$ (e) $(m - n)(j + y)$ (f) $(3y - z)(3x + 4p)$