1. Factorise each expression step-by-step. **a) $64a^2b^3 - 16b^2a^3$** - Extract common factors: $16a^2b^2(4b - a)$ **b) $pq + qr - pq + r$** - Simplify: $pq - pq = 0$, so expression is $qr + r$ - Factor out $r$: $r(q + 1)$ **c) $3mr - 24$** - Factor out 3: $3(mr - 8)$ **d) $b^4 - ab^3 + b^2c$** - Factor out $b^2$: $b^2(b^2 - ab + c)$ **e) $a^4 - 169$** - Recognize difference of squares: $a^4 - 13^2$ - Write $a^4$ as $(a^2)^2$, so factorise: $$ (a^2 - 13)(a^2 + 13) $$ **f) $9ab^2 - 3abc$** - Factor out $3ab$: $3ab(3b - c)$ **g) $81 - z^2$** - Difference of squares: $9^2 - z^2$ - Factorise: $$ (9 - z)(9 + z) $$ **h) $36m^2 - 25n^2$** - Difference of squares: $(6m)^2 - (5n)^2$ - Factorise: $$ (6m - 5n)(6m + 5n) $$ **i) $m^2n + 3mn - 2mn^2$** - Factor out $mn$: $mn(m + 3 - 2n)$ **j) $121p^2 - 9q^2$** - Difference of squares: $(11p)^2 - (3q)^2$ - Factorise: $$ (11p - 3q)(11p + 3q) $$ **k) $144x^2 - 108y^2 - 60z^2$** - Factor out 12: $12(12x^2 - 9y^2 - 5z^2)$ **l) $64a^2b^2 - 49c^2d^2$** - Difference of squares: $(8ab)^2 - (7cd)^2$ - Factorise: $$ (8ab - 7cd)(8ab + 7cd) $$ Final answers: a) $16a^2b^2(4b - a)$ b) $r(q + 1)$ c) $3(mr - 8)$ d) $b^2(b^2 - ab + c)$ e) $(a^2 - 13)(a^2 + 13)$ f) $3ab(3b - c)$ g) $(9 - z)(9 + z)$ h) $(6m - 5n)(6m + 5n)$ i) $mn(m + 3 - 2n)$ j) $(11p - 3q)(11p + 3q)$ k) $12(12x^2 - 9y^2 - 5z^2)$ l) $(8ab - 7cd)(8ab + 7cd)$