Answer:
We have, \[63({{p}^{4}}+5{{p}^{3}}-24{{p}^{2}})\div 9p(p+8)\] \[=\frac{63({{p}^{4}}+5{{p}^{3}}-24{{p}^{2}})}{9p(P+8)}\] \[=\frac{63{{p}^{2}}({{p}^{2}}+5p-24)}{9p(p+8)}\] \[=\frac{63{{p}^{2}}}{9p}\left[ \frac{({{p}^{2}}+5p-24)}{(p+8)} \right]\] \[=7p\left[ \frac{{{p}^{2}}+8p-3p-24}{p+8} \right]\] \[=7p\left[ \frac{p(p+8)-3(p+8)}{(p+8)} \right]\] \[=7p\left[ \frac{(p+8)(p-3)}{(p+8)} \right]\] \[=7p(p-3)\].
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