Question

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

• A. $28+5p-18q+8pq-2q^2+p^{2}q-5p{q}^2$
• B. $8+11p-18q+8pq-2q^2+p^{2}q-5p{q}^2$
• C. $28-5p+18q-8pq+2q^2-p^{2}q+5p{q}^2$
• D. none

Answer 1

The correct option is A $28+5p-18q+8pq-2q^2+p^{2}q-5p{q}^2$

We subtract the given expression $4p^{2}q-3pq+5p{q}^2-8p+7q-10$ from $18-3p-11q+5pq-2q^2+5p^{2}q$ as shown below:

$(18-3p-11q+5pq-2q^2+5p^{2}q)-(4p^{2}q-3pq+5p{q}^2-8p+7q-10)=18-3p-11q+5pq-2q^2+5p^{2}q-4p^{2}q+3pq-5p{q}^2+8p-7q+10=(18+10)+(-3p+8p)+(-11q-7q)+(5pq+3pq)-2q^2+(5p^{2}q-4p^{2}q)-5p{q}^2\left(Combiningliketerms\right)=28+5p-18q+8pq-2q^2+p^{2}q-5p{q}^2$

Hence, $(18-3p-11q+5pq-2q^2+5p^{2}q)-(4p^{2}q-3pq+5p{q}^2-8p+7q-10)=28+5p-18q+8pq-2q^2+p^{2}q-5p{q}^2$.