(a) Subtract $4a-7ab + 3b + 12$ from $12a – 9ab + 5b – 3$

(b) Subtract $3xy + 5yz – 7zx$ from $5xy – 2yz – 2zx + 10xyz$

(c) Subtract $4p^{2}q – 3pq + 5p{q}^2 – 8p + 7q – 10 \text{from} 18 – 3p – 11q + 5pq – 2p{q}^2 + 5p^{2}q$

a) Consider the given expression  $4a-7ab + 3b + 12$ and $12a – 9ab + 5b – 3$.

Perform subtraction to get the following,

$(12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)$

$= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12$

$= 12a – 4a -9ab + 7ab +5b – 3b -3 -12$

$= 8a – 2ab + 2b – 15$

Hence, the simplification of the given expression is $8a – 2ab + 2b – 15$.

b) Consider the given expression  $3xy + 5yz – 7zx$ from $5xy – 2yz – 2zx + 10xyz$.

Perform subtraction to get the following,

$(5xy – 2yz – 2zx + 10xyz) – (3xy + 5yz – 7zx)$

$= 5xy – 2yz – 2zx + 10xyz – 3xy – 5yz + 7zx$

$=5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz$

$= 2xy – 7yz + 5zx + 10xyz$

Hence, the simplification of the given expression is $2xy – 7yz + 5zx + 10xyz$.

c) Consider the given expression $4p^{2}q – 3pq + 5p{q}^2 – 8p + 7q – 10 \text{from} 18 – 3p – 11q + 5pq – 2p{q}^2 + 5p^{2}q$.

Perform subtraction to get the following,

$(18-3p-11q+5pq- 2p{q}^2+5p^{2}q)- (4p^{2}q-3pq + 5p{q}^2 - 8p+7q -10)$

$= 18- 3p-11q + 5pq-2p{q}^2+5p^{2}q-4p^{2}q+3pq-5p{q}^2+8p-7q+10$

$=18+10-3p+8p-11q–7q+5pq+3pq-2p{q}^2–5p{q}^2+5p^{2}q–4p^{2}q$

$=28+5p-18q + 8pq-7p{q}^2+p^{2}q$

Hence, the simplification of the given expression is $28+5p-18q + 8pq-7p{q}^2+p^{2}q$.