Question

what should be subtracted from 3r²p-2pq²+qr² to get 2r²p+4pq²-3qr².

Answer 1

${r}^{2} p - 6p {q}^{2} + 4q {r}^{2}$

Answer 2

Let the required number be x
According to the question
$3 {r}^{2} p - 2p {q}^{2} + q {r}^{2} - x = 2 {r}^{2} p + 4p {q}^{2} - 3q {r}^{2} \\ 3 {r}^{2} p - 2p {q}^{2} + q {r}^{2} - 2 {r}^{2} p - 4p {q}^{2} + 3q {r}^{2} = x \\ x = {r}^{2} p - 6p {q}^{2} + 4q {r}^{2}$