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Mathematics

Find the excess of 4p2 - 2pq + 3q2 over 2p2 - pq + 4q2.

Algebraic Expressions

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Answer

"Excess" means how much larger the first expression is than the second. To find it, we subtract the second from the first (A - B).

∴ Subtract 2p2 - pq + 4q2 from 4p2 - 2pq + 3q2.

4p22pq+3q2+2p2pq+4q22p2+2p2pqq2\begin{array}{rcccc} 4p^2 & - & 2pq & + & 3q^2 \\ +2p^2 & - & pq & + & 4q^2 \\ -\phantom{2p^2} & + & & - \\ \hline 2p^2 & - & pq & - & q^2 \\ \hline \end{array}

Hence, the answer is 2p2 - pq - q2

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