• # question_answer What must be subtracted from $\mathbf{4p}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-2pq-v+5}\,\,\mathbf{to}\,\,\mathbf{get}\,\,\mathbf{-}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{+pq-8}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-2v+6}$? A) $4p{{x}^{2}}+3{{q}^{2}}-3pq+v-1$B) $5{{q}^{2}}-3pq+8pq+2{{q}^{2}}+v-1$C) $-5\,{{p}^{2}}+3pq-2{{q}^{2}}-v+1$          D) $-3{{p}^{2}}+p\,q+14{{q}^{2}}+3v-11$E) None of these

Explanation Option [a] is correct. Let us consider, x be an expression subtracted from the following expressions to get a result as given. \begin{align} & \Rightarrow x=\left( 4p\,{{x}^{2}}-2pq-6{{q}^{2}}-v+5 \right)-\left( -{{q}^{2}}+pq-8\,{{q}^{2}}-2v+6 \right) \\ & =4\,p\,{{x}^{2}}-2\,p\,q\,-6\,{{q}^{2}}-v+5+{{q}^{2}}-p\,q+8\,{{q}^{2}}+2v-6=4p{{x}^{2}}+3{{q}^{2}}-3pq+v-1 \\ \end{align}