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# Add in a vertical arrangement. (1) p2 − 2p + 7; p3 + 2p2 + 3 (2) m2 − 3m − 9; m3 + 5m − 4 (3) 2x3 − 3x2y + 5xy2 − 4y3; −x3 + 2x2y − 4xy2 + 3y3

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Solution

## (1) p2 − 2p + 7; p3 + 2p2 + 3 $\begin{array}{c}\begin{array}{cccccccc}& & & {p}^{2}& -& 2p& +& 7\end{array}\\ \begin{array}{cccccccc}+& {p}^{3}& +& 2{p}^{2}& +& 0p& +& 3\end{array}\\ \overline{)\overline{)\begin{array}{cccccccc}& {p}^{3}& +& 3{p}^{2}& -& 2p& +& 10\end{array}}}\end{array}\phantom{\rule{0ex}{0ex}}$ (2) m2 − 3m − 9; m3 + 5m − 4 $\begin{array}{c}\begin{array}{cccccccc}& & & {m}^{2}& -& 3m& -& 9\end{array}\\ \begin{array}{cccccccc}+& {m}^{3}& +& 0{m}^{2}& +& 5m& -& 4\end{array}\\ \overline{)\overline{)\begin{array}{cccccccc}& {m}^{3}& +& {m}^{2}& +& 2m& -& 13\end{array}}}\end{array}$ (3) 2x3 − 3x2y + 5xy2 − 4y3; −x3 + 2x2y − 4xy2 + 3y3 $\begin{array}{c}\begin{array}{cccccccc}& 2{x}^{3}& -& 3{x}^{2}y& +& 5x{y}^{2}& -& 4{y}^{3}\end{array}\\ \begin{array}{cccccccc}+& \left(-\right){x}^{3}& +& 2{x}^{2}y& -& 4x{y}^{2}& +& 3{y}^{3}\end{array}\\ \overline{)\overline{)\begin{array}{cccccccc}& {x}^{3}& -& {x}^{2}y& +& x{y}^{2}& -& {y}^{3}\end{array}}}\end{array}$

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